Decoding apparatus and method, and program

Technical Field

0001The present technology relates to a decoding apparatus, a decoding method and a program, and, more particularly, a decoding apparatus, a decoding method and a program which make it possible to obtain sound with higher quality.

Background Art

0002In related art, in an audio coding technique of moving picture experts group (MPEG) advanced audio coding (AAC) (ISO/IEC14496-3:2001), it is possible to record auxiliary information of downmixing or dinamic range compression (DRC) in a bit stream and use the auxiliary information at a reproduction side according to an environment of the reproduction side (see, for example, Non-Patent Literature 1).

0003Use of such auxiliary information enables an audio signal to be downmixed at the reproduction side or volume to be appropriately controlled through the DRC.

Citation List

0004Non-Patent Literature 1: Information technology Coding of audiovisual objects Part 3: Audio (ISO/IEC 14496-3:2001)

0005<patcit id="pcit0001" dnum="US2010083344A1"><text>US 2010/083344 A1</text></patcit> describes a method and a system for transcoding audio gain metadata related to dynamic range control from first gain metadata of a first audio coding scheme to second gain metadata of a second audio coding scheme, wherein the first and second audio coding schemes use coding blocks and wherein each coding block has at least one associated gain value. The method and the system select a gain value of the second gain metadata based on the gain values of the first gain metadata such that within a time interval around the time instance associated with the gain value of the second gain metadata, the minimum gain value of the first gain metadata is selected.

0006Further non-patent literature can be found in<nplcit id="ncit0001" npl-type="s"><text> KRISTOFER KJÖRLING ET AL, "Proposed modification of 14496-3:2001/AMD1:2003/DCor.1. (N6008) concerning SBR and DRC", 67. MPEG MEETING; 08-12-2003 - 12-12-2003; WAIKOLOA; (MOTION PICTURE EXPERT GROUP OR ISO/IEC JTC1/SC29/WG11), (20031203), no. M10373, ISSN 0000-0260, XP030039228</text></nplcit>.

Summary of Invention

Technical Problem

0007For example, with the above-described coding technique, it is possible to designate DRC gain information for volume control as auxiliary information of DRC in units of a frame of an audio signal, and, at a reproduction side, by correcting volume of the audio signal based on this DRC gain information, it is possible to obtain sound with appropriate volume.

0008However, a gain indicated by such DRC gain information becomes the same value for each sample within one frame of the audio signal which is a temporal signal. That is, all samples included in one frame are corrected with the same gain.

0009Therefore, for example, when a magnitude of the gain indicated by the DRC gain information largely changes between frames, portions of temporal waveforms of the audio signal become discontinuous between the frames, which may cause degradation in auditory terms.

0010The present technology has been made in view of such circumstances, and is directed to making it possible to obtain sound with higher quality.

Solution to Problem

0011A decoding apparatus, method and program as defined in the independent claims are provided.

Advantageous Effects of Invention

0012According to the claimed subject-matter, it is possible to obtain sound with higher quality.

0013Note that advantageous effects are not limited to the advantageous effect described herein and may be any advantageous effects described in the present disclosure.

Brief Description of Drawings

0014<ul id="ul0001" list-style="none" compact="compact"><li>[<figref idref="f0001">FIG. 1] FIG. 1</figref> is a diagram for explaining linear interpolation of a gain according to an embodiment of the present technology.</li><li>[<figref idref="f0001">FIG. 2] FIG. 2</figref> is a diagram illustrating an example of a gain waveform according to an embodiment of the present technology.</li><li>[<figref idref="f0002">FIG. 3] FIG. 3</figref> is a diagram for explaining non-linear interpolation of a gain according to an embodiment of the present technology.</li><li>[<figref idref="f0003">FIG. 4] FIG. 4</figref> is a diagram illustrating a configuration example of an encoding apparatus.</li><li>[<figref idref="f0004">FIG. 5] FIG. 5</figref> is a flowchart explaining encoding processing.</li><li>[<figref idref="f0005">FIG. 6] FIG. 6</figref> is a diagram illustrating DRC characteristics according to an embodiment of the present technology.</li><li>[<figref idref="f0006">FIG. 7] FIG. 7</figref> is a diagram illustrating a configuration example of a decoding apparatus according to an embodiment of the present technology.</li><li>[<figref idref="f0007">FIG. 8] FIG. 8</figref> is a flowchart explaining decoding processing according to an embodiment of the present technology.</li><li>[<figref idref="f0008">FIG. 9] FIG. 9</figref> is a flowchart explaining gain decoding processing according to an embodiment of the present technology.</li><li>[<figref idref="f0009">FIG. 10] FIG. 10</figref> is a diagram illustrating a configuration example of a decoding apparatus according to an embodiment of the present technology.</li><li>[<figref idref="f0010">FIG. 11] FIG. 11</figref> is a flowchart explaining gain decoding processing according to an embodiment of the present technology.</li><li>[<figref idref="f0011">FIG. 12] FIG. 12</figref> is a diagram for explaining interpolation of a gain waveform according to an embodiment of the present technology.</li><li>[<figref idref="f0011">FIG. 13] FIG. 13</figref> is a diagram for explaining interpolation of a gain waveform according to an embodiment of the present technology.</li><li>[<figref idref="f0012">FIG. 14] FIG. 14</figref> is a diagram for explaining interpolation of a gain waveform according to an embodiment of the present technology.</li><li>[<figref idref="f0013">FIG. 15] FIG. 15</figref> is a diagram illustrating a configuration example of a decoding apparatus according to an embodiment of the present technology.</li><li>[<figref idref="f0014">FIG. 16] FIG. 16</figref> is a flowchart explaining gain decoding processing according to an embodiment of the present technology.</li><li>[<figref idref="f0015">FIG. 17] FIG. 17</figref> is a diagram explaining interpolation of a gain waveform according to an embodiment of the present technology.</li><li>[<figref idref="f0016">FIG. 18] FIG. 18</figref> is a flowchart explaining gain decoding processing according to an embodiment of the present technology.</li><li>[<figref idref="f0017">FIG. 19] FIG. 19</figref> is a diagram illustrating a configuration example of a computer according to an embodiment of the present technology.</li></ul>

Description of Embodiments

0015Hereinafter, an embodiment to which the present technology is applied will be described with reference to drawings.

<First Embodiment>

<Outline of the Present Technology>

0016The present technology relates to a technique of encoding a gain value when volume of an audio signal is corrected at a reproduction side, multiplexing a gain code string obtained by encoding the gain value and a signal code string obtained by encoding the audio signal and transmitting the multiplexed code string, and a technique of decoding these gain code string and signal code string and correcting volume of the audio signal.

0017In the present technology, by designating an arbitrary value for each sample within a frame of the audio signal as a gain value for volume correction, it is possible to obtain sound with a smoother temporal waveform. By this means, it is possible to obtain sound with higher quality which does not cause a feeling of strangeness. Here, while the gain value for volume correction may be a dB value or a linear value, description will be continued below assuming that the gain value is a linear value.

0018Further, when the gain value is encoded, if a gain code string is obtained by encoding only gain values at part of sample positions such as, for example, characteristic positions such as inflection points of a gain waveform and gain values which are arranged at predetermined intervals among gain values at respective sample positions within a frame, it is also possible to reduce a code amount of the gain code string.

0019In this case, a decoding side of the gain code string needs to obtain an original gain waveform based on gain values at some sample positions obtained through decoding of the gain code string.

0020Here, as a method for obtaining the original gain waveform, for example, there is a possible method for obtaining gain values at sample positions which are not included in the gain code string by performing linear interpolation as illustrated in <figref idref="f0001">FIG. 1</figref>.

0021It should be noted that <figref idref="f0001">FIG. 1</figref> indicates a gain value on a vertical axis and a sample position within a frame of an audio signal on a horizontal axis.

0022Further, hereinafter, a sample position of an encoded gain value which is included in a gain code string will be also specially referred to as a gain sample position. Still further, in the following, a point on a gain waveform expressed with an encoded sample position and a gain value included in the gain code string will be also simply referred to as a gain sample position.

0023In the example of <figref idref="f0001">FIG. 1</figref>, information of a gain sample position G11 and a gain sample position G12 is obtained through decoding of the gain code string.

0024Here, a gain value at the k-th gain sample position within a frame is set as g[k], and a sample length (the number of samples) in a sample axis direction from the k-th gain sample position to the k+1-th gain sample position will be expressed as T[k].

0025In this case, when it is assumed that a sample position of the k-th gain sample position G11 is n = 0, the gain sample position G11 is a point expressed with a coordinate (0, g[k]), and the gain sample position G12 is a point expressed with a coordinate (T[k], g[k+1]). Here, n is an index indicating the n-th sample position from the head of the frame.

0026Further, a gain waveform between the gain sample position G11 and the gain sample position G12 obtained through linear interpolation becomes a waveform indicated with a straight line L11. That is, between the gain sample position G11 and the gain sample position G12, a gain value at each sample position is obtained through interpolation assuming that the gain value linearly changes.

0027However, if the gain waveform is estimated through linear interpolation, for example, as indicated with a curve C11 in <figref idref="f0001">FIG. 2</figref>, when a smooth gain waveform is tried to be encoded, the number of points to be encoded in the gain waveform, that is, the number of gain sample positions increases. It should be noted that <figref idref="f0001">FIG. 2</figref> indicates a gain value on a vertical axis and a sample position within a frame of an audio signal on a horizontal axis.

0028In this example, because the gain waveform indicated with the curve C11 is a smooth waveform, if the decoding side tries to reproduce the gain waveform with a certain level of precision, it is necessary to encode gain values at a number of gain sample positions. This will increase a code amount of a bit stream obtained by multiplexing the gain code string and the signal code string, that is, increase a bit rate.

0029Therefore, in the present technology, in order to make it possible to obtain sound with higher quality with a less code amount, non-linear interpolation is newly performed as appropriate in addition to linear interpolation. That is, a gain waveform is generated by performing interpolation processing using a more appropriate method selected between linear interpolation and non-linear interpolation. It should be noted that non-linear interpolation can be, for example, interpolation using a quadratic function or a cubic function.

0030For example, when non-linear interpolation utilizing a cubic function is performed, a waveform indicated with a curve C21 in <figref idref="f0002">FIG. 3</figref> can be obtained as a gain waveform between the gain sample position G11 and the gain sample position G12 illustrated in <figref idref="f0001">FIG. 1</figref>. It should be noted that <figref idref="f0002">FIG. 3</figref> indicates a gain value on a vertical axis and a sample position within a frame of an audio signal on a horizontal axis. Further, in <figref idref="f0002">FIG. 3</figref>, the same reference numerals as those in <figref idref="f0001">FIG. 1</figref> are assigned to portions corresponding to those in <figref idref="f0001">FIG. 1</figref>, and explanation thereof will be omitted as appropriate.

0031In this example, the gain code string includes information indicating the sample position, the gain value and a gain inclination value at the gain sample position G11, and information indicating the sample position, the gain value and a gain inclination value at the gain sample position G12.

0032Here, the gain inclination value is information indicating inclination of the original gain waveform at a gain sample position. Hereinafter, a gain inclination value at the k-th gain sample position will be expressed as s[k].

0033In <figref idref="f0002">FIG. 3</figref>, an arrow D11 indicates the gain inclination value s[k] at the gain sample position G11, and an arrow D12 indicates a gain inclination value s[k+1] at the gain sample position G12.

0034At the decoding side, the gain waveform between the gain sample position G11 and the gain sample position G12 is obtained through non-linear interpolation utilizing a cubic function, and, as a result, the gain waveform indicated with the curve C21 is obtained.

0035The gain waveform indicated with the curve C21 is, for example, a curve of a cubic function which passes through the gain sample position G11 and the gain sample position G12 and whose inclination at the gain sample position G11 and the gain sample position G12 is respectively s[k] and s[k+1].

0036In this manner, by utilizing non-linear interpolation as appropriate, even when the gain waveform is a smooth waveform, it is possible to reproduce the gain waveform with high precision through encoding of less gain sample positions, that is, with a less code amount.

0037In the present technology, for example, as a parameter for switching between linear interpolation and non-linear interpolation, interpolation mode information indicating an interpolation scheme using linear interpolation or an interpolation scheme using non-linear interpolation is included in the gain code string. The decoding side switches between linear interpolation and non-linear interpolation according to this interpolation mode information.

0038Here, the interpolation mode information may be, for example, an index of two bits for switching among linear interpolation, interpolation using a quadratic function and interpolation using a cubic function, or may be a flag of one bit for switching between linear interpolation and interpolation using a cubic function which is non-linear interpolation. That is, any information may be used as the interpolation mode information if the information indicates a method for interpolating a gain waveform.

0039Further, in the present technology, when the interpolation mode information is information indicating an interpolation scheme using non-linear interpolation, in addition to a gain value, a gain inclination value is included in the gain code string for each gain sample position.

0040Here, the gain inclination value s[k] indicates change of a gain value per one sample. For example, the gain inclination value s[k] at the k-th gain sample position is inclination of a straight line which connects a point on the gain waveform at the k-th gain sample position and a point on the gain waveform at the next sample position of the k-th gain sample position. It should be noted that the gain inclination value may be obtained using any method if the gain inclination value indicates inclination at the gain sample position on the gain waveform.

0041It should be noted that the gain inclination value as is may be stored in the gain code string, or a quantization value of the gain inclination value or an entropy encoded value such as a Huffman encoded value of the gain inclination value may be stored in the gain code string.

<Linear Interpolation>

0042Further, specific examples of a method for performing linear interpolation and a method for performing non-linear interpolation on a gain value at each sample position between two gain sample positions will be described. First, a method for performing linear interpolation will be described.

0043When linear interpolation is performed using the interpolation mode information, at the decoding side, a gain value is read out for each gain sample position from the gain code string.

0044Here, an index at the k-th gain sample position is set as k, and a gain value at the k-th gain sample position read out from the gain code string is set as g[k]. Further, a sample length between the k-th gain sample position and the k+1-thgain sample position is set as T[k], and it is assumed that the sample length T[k] is included in the gain code string as information indicating the sample position of the k+1-th gain sample position.

0045It is now assumed that the k-th gain sample position is a head position of a frame, that is, the sample position of n = 0. In such a case, a gain value g_interpolated[n] of the sample n which is located between the k-th gain sample position and the k+1-th gain sample position and which is the n-th (where 0 ≤ n &lt; t[k]) sample from the head is calculated using the following equation (1). [Math. 1] <maths id="math0001" num="(1)"><math display="block"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">g</mi><mo>_</mo><mi>interpolated</mi><mfenced open="[" close="]"><mi mathvariant="normal">n</mi></mfenced><mo>=</mo><mi mathvariant="normal">a</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>×</mo><mi mathvariant="normal">n</mi><mo>+</mo><mi mathvariant="normal">b</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mtd></mtr><mtr><mtd><mfenced><mn>0</mn><mo>≤</mo><mi mathvariant="normal">n</mi><mo>&lt;</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced></mtd></mtr></mtable></math><img file="EP3608909B1_D0001.tif" /></maths>

0046It should be noted that in equation (1), a[k] and b[k] are values respectively obtained using the following equation (2) and equation (3). Math. 2] <maths id="math0002" num="(2)"><math display="block"><mi mathvariant="normal">a</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mfenced><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>/</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></math><img file="EP3608909B1_D0002.tif" /></maths>

0047[Math. 3] <maths id="math0003" num="(3)"><math display="block"><mi mathvariant="normal">b</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></math><img file="EP3608909B1_D0003.tif" /></maths>

0048That is, a[k] and b[k] indicate inclination and intercept of a straight line connecting the k-th gain sample position and the k+1-th gain sample position. Therefore, in this example, as described with reference to <figref idref="f0001">FIG. 1</figref>, it is determined that the gain value linearly changes between the k-th gain sample position and the k+1-th gain sample position, and a gain value of each sample n is obtained through linear interpolation.

<Non-Linear Interpolation>

0049Subsequently, a case will be described where a gain value of the sample n between the k-th gain sample position and the k+1-th gain sample position is obtained through non-linear interpolation. Here, description will be continued with a case where interpolation using a cubic function is performed as an example of non-linear interpolation.

0050When non-linear interpolation is performed according to the interpolation mode information, at the decoding side, a gain value and a gain inclination value are read out from the gain code string for each gain sample position.

0051Here, in a similar manner to a case of linear interpolation, a gain value at the k-th gain sample position is set as g[k], and a sample length between the k-th gain sample position and the k+1-th gain sample position is set as T[k]. Further, a gain inclination value at the k-th gain sample position is set as s[k].

0052It is now assumed that the k-th gain sample position is a head position of the frame, that is, a sample position of n = 0. In such a case, a gain value g_interpolated[n] of the sample n which is located between the k-th gain sample position and the k+1-th gain sample position and which is the n-th (where 0 ≤ n &lt; T[k]) sample from the head is calculated using the following equation (4). [Math. 4] <maths id="math0004" num="(4)"><math display="block"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">g</mi><mo>_</mo><mi>interpolated</mi><mfenced open="[" close="]"><mi mathvariant="normal">n</mi></mfenced><mo>=</mo><mi mathvariant="normal">c</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>×</mo><msup><mi mathvariant="normal">n</mi><mn>3</mn></msup><mo>+</mo><mi mathvariant="normal">d</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>×</mo><msup><mi mathvariant="normal">n</mi><mn>2</mn></msup><mo>+</mo><mi mathvariant="normal">e</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>×</mo><mi mathvariant="normal">n</mi><mo>+</mo><mi mathvariant="normal">f</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mtd></mtr><mtr><mtd><mfenced><mn>0</mn><mo>≤</mo><mi mathvariant="normal">n</mi><mo>&lt;</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced></mtd></mtr></mtable></math><img file="EP3608909B1_D0004.tif" /></maths>

0053It should be noted that, in equation (4), c[k], d[k], e[k] and f[k] are values respectively obtained using the following equation (5) to equation (8). [Math. 5] <maths id="math0005" num="(5)"><math display="block"><mi mathvariant="normal">c</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mfenced><mn>1</mn><mo>/</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>×</mo><mfenced open="{" close="}"><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>+</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>/</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mn>2</mn><mo>×</mo><mfenced><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>/</mo><mfenced><mi mathvariant="normal">T</mi><msup><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mn>2</mn></msup></mfenced></mfenced></math><img file="EP3608909B1_D0005.tif" /></maths>

0054[Math. 6] <maths id="math0006" num="(6)"><math display="block"><mi mathvariant="normal">d</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mn>3</mn><mo>×</mo><mfenced><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>−</mo><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>+</mo><mn>2</mn><mo>×</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>/</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></math><img file="EP3608909B1_D0006.tif" /></maths>

0055[Math. 7] <maths id="math0007" num="(7)"><math display="block"><mi mathvariant="normal">e</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></math><img file="EP3608909B1_D0007.tif" /></maths>

0056[Math. 8] <maths id="math0008" num="(7)"><math display="block"><mi mathvariant="normal">f</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></math><img file="EP3608909B1_D0008.tif" /></maths>

0057In this example, as described with reference to <figref idref="f0002">FIG. 3</figref>, a gain value of each sample n is obtained through non-linear interpolation, that is, interpolation using a cubic function assuming that the gain value changes according to a cubic function indicated in equation (4) between the k-th gain sample position and the k+1-th gain sample position.

0058As described above, by obtaining a gain value as appropriate through non-linear interpolation, a smooth gain waveform as illustrated in, for example, <figref idref="f0001">FIG. 2</figref> can be encoded at a lower bit rate, so that it is possible to improve coding efficiency.

<Configuration Example of Encoding Apparatus>

0059Subsequently, a specific example, not according to the present invention but useful for understanding the invention, to which the present technology described above is applied will be described.

0060<figref idref="f0003">FIG. 4</figref> is a diagram illustrating a configuration example of an encoding apparatus to which the present technology is applied.

0061The encoding apparatus 11 has a sound pressure level calculating circuit 21, a gain calculating circuit 22, a gain encoding circuit 23, a signal encoding circuit 24 and a multiplexing circuit 25.

0062The sound pressure level calculating circuit 21 calculates sound pressure levels of channels constituting an input time series signal based on the input time series signal which is a supplied multichannel audio signal and obtains a representative value of sound pressure levels for each of the channels as a representative sound pressure level.

0063It should be noted that the representative value of the sound pressure levels is obtained for each frame of the input time series signal. Further, a frame which is used as a processing unit at the sound pressure level calculating circuit 21 is synchronized with a frame of the input time series signal which is to be processed at the signal encoding circuit 24 which will be described later and is made a frame having a length shorter than that of a frame at the signal encoding circuit 24.

0064The sound pressure level calculating circuit 21 supplies the obtained representative sound pressure level to the gain calculating circuit 22. The representative sound pressure level obtained in this manner indicates a representative sound pressure level of the channels of the input time series signal which is constituted with an audio signal of the predetermined number of channels such as, for example, 11.1 ch.

0065The gain calculating circuit 22 calculates a gain value based on the representative sound pressure level supplied from the sound pressure level calculating circuit 21 and supplies the gain value to the gain encoding circuit 23.

0066Here, the gain value indicates a gain value for correcting volume of the input time series signal so as to be able to obtain sound of appropriate volume when the input time series signal is reproduced at the decoding side, and a gain value is calculated for each sample position within a frame at the gain calculating circuit 22.

0067The gain encoding circuit 23 encodes the gain value supplied from the gain calculating circuit 22 and supplies a gain code string obtained as a result of encoding to the multiplexing circuit 25.

0068Here, the gain code string includes gain information for obtaining a gain value of each gain sample position and interpolation mode information.

0069The signal encoding circuit 24 encodes the supplied input time series signal using a predetermined encoding scheme, for example, a typical encoding method typified by an encoding method using MEPG AAC and supplies a signal code string obtained as a result of encoding to the multiplexing circuit 25.

0070The multiplexing circuit 25 multiples the gain code string supplied from the gain encoding circuit 23 and the signal code string supplied from the signal encoding circuit 24 and outputs an output code string obtained as a result of multiplexing.

<Description of Encoding Processing>

0071Specific operation of the encoding apparatus 11 will be described next.

0072When the input time series signal corresponding to one frame is supplied, the encoding apparatus 11 performs encoding processing of encoding the input time series signal and outputting the output code string. Hereinafter, encoding processing by the encoding apparatus 11 will be described with reference to the flowchart of <figref idref="f0004">FIG. 5</figref>.

0073In step S11, the sound pressure level calculating circuit 21 calculates a representative sound pressure level of the input time series signal based on the supplied input time series signal and supplies the representative sound pressure level to the gain calculating circuit 22.

0074Specifically, the sound pressure level calculating circuit 21 calculates sound pressure levels of respective channels constituting the input time series signal and sets a representative value of the sound pressure levels of these channels as a representative sound pressure level.

0075For example, in a method for calculating a sound pressure level, a maximum value, a root mean square (RMS), or the like, of frames of an audio signal of channels constituting the input time series signal is used, and a sound pressure level is obtained for each of the channels constituting the input time series signal for the frames of the input time series signal.

0076Further, as a method for calculating a representative value as the representative sound pressure level, for example, a method in which a maximum value among sound pressure levels of the channels in the same frame is set as the representative value, a method in which one representative value is calculated using a specific calculation formula from the sound pressure levels of the channels, or the like, can be used. Specifically, for example, it is possible to calculate the representative value using a loudness calculation formula described in ITU-R BS.1770-2(03/2011).

0077In step S12, the gain calculating circuit 22 calculates a gain value based on the representative sound pressure level supplied from the sound pressure level calculating circuit 21 and supplies the gain value to the gain encoding circuit 23.

0078For example, the gain calculating circuit 22 calculates the gain value according to DRC characteristics designated by a higher-order control apparatus.

0079The DRC characteristics designated by the higher-order control apparatus can be DRC characteristics as illustrated in, for example, <figref idref="f0005">FIG. 6</figref>. It should be noted that <figref idref="f0005">FIG. 6</figref> indicates an input sound pressure level (dBFS), that is, a representative sound pressure level on a horizontal axis, and indicates an output sound pressure level (dBFS), that is, a corrected sound pressure level when the sound pressure level (volume) of the input time series signal is corrected, on a vertical axis.

0080A broken line L31 and a broken line L32 respectively indicate relationship of the input and output sound pressure levels. For example, according to the DRC characteristic indicated with the broken line L31, when there is an input of the representative sound pressure level of 0 dBFS, volume is corrected so that the sound pressure level of the input time series signal becomes -27 dBFS.

0081On the other hand, for example, according to the DRC characteristics indicated with the broken line L32, when there is an input of the representative sound pressure level of 0 dBFS, volume is corrected so that the sound pressure level of the input time series signal becomes -21 dBFS.

0082The gain calculating circuit 22 determines a gain value according to the DRC characteristics indicated with such a broken line L31 and a broken line L32. This gain value is outputted as a gain waveform synchronized with the frame at the signal encoding circuit 24. That is, the gain calculating circuit 22 calculates a gain value for each of samples constituting a frame which is to be processed of the input time series signal.

0083More specifically, for example, the gain calculating circuit 22 obtains a gain waveform g(J, n) in a frame J by performing calculation of the following equation (9). [Math. 9] <maths id="math0009" num="(9)"><math display="block"><mi mathvariant="normal">g</mi><mfenced><mi mathvariant="normal">J</mi><mi mathvariant="normal">n</mi></mfenced><mo>=</mo><mi mathvariant="normal">A</mi><mo>×</mo><mi>Gt</mi><mfenced><mi mathvariant="normal">J</mi></mfenced><mo>+</mo><mfenced><mn>1</mn><mo>−</mo><mi mathvariant="normal">A</mi></mfenced><mo>×</mo><mi mathvariant="normal">g</mi><mfenced><mi mathvariant="normal">J</mi><mo>,</mo><mi mathvariant="normal">n</mi><mo>−</mo><mn>1</mn></mfenced></math><img file="EP3608909B1_D0009.tif" /></maths>

0084It should be noted that, in equation (9), n indicates a position of a sample which takes values from 0 to N-1 when a frame length is set as N, Gt(J) indicates the above-described DRC characteristics, that is, a target gain in the frame J determined by the input sound pressure level and the output sound pressure level.

0085Further, A in equation (9) is a value determined by the following equation (10). [Math. 10] <maths id="math0010" num="(10)"><math display="block"><mi mathvariant="normal">A</mi><mo>=</mo><mn>1</mn><mo>−</mo><mi>exp</mi><mfenced><mo>−</mo><mn>1</mn><mo>/</mo><mfenced><mn>2</mn><mo>×</mo><mi>Fs</mi><mo>×</mo><mi>Tc</mi><mfenced><mi mathvariant="normal">J</mi></mfenced></mfenced></mfenced></math><img file="EP3608909B1_D0010.tif" /></maths>

0086In equation (10), Fs indicates a sampling frequency (Hz), Tc(J) indicates a time constant in the frame J, and exp(x) indicates an exponent function. Further, in equation (9), a gain value of the last sample in a frame immediately before the frame is used as a gain waveform g(J, n-1) when n = 0.

0087Returning to explanation of the flowchart in <figref idref="f0004">FIG. 5</figref>, in step S13, the gain encoding circuit 23 performs gain encoding processing to encode the gain value supplied from the gain calculating circuit 22. The gain encoding circuit 23 then supplies the gain code string obtained through the gain encoding processing to the multiplexing circuit 25.

0088For example, the gain encoding circuit 23 extracts a gain sample position to be encoded from the gain value at each sample position supplied from the gain calculating circuit 22, that is, a gain waveform of the frame to be processed. For example, characteristic samples such as inflection points in the gain waveform may be used as the gain sample positions, or samples arranged at predetermined intervals may be used as the gain sample positions.

0089The gain encoding circuit 23 generates interpolation mode information and gain information for each of the gain sample positions extracted in this manner.

0090For example, the gain encoding circuit 23 generates the interpolation mode information by performing so-called local decoding.

0091That is, the gain encoding circuit 23 generates a gain waveform between two gain sample positions adjacent to each other through interpolation for linear interpolation and non-linear interpolation, and calculates a difference between the gain waveform and an actual gain waveform. The gain encoding circuit 23 then generates information indicating an interpolation scheme in which the obtained difference is smaller as the interpolation mode information.

0092It should be noted that whether linear interpolation is performed or non-linear interpolation is performed may be determined using any other method. For example, it is also possible to determine that linear interpolation is performed when the gain value is the same between the gain sample position to be processed and the gain sample position immediately before the gain sample position to be processed, and the gain inclination value of the gain sample position immediately before the gain sample position to be processed is 0, and, that non-linear interpolation is performed in other cases. Alternatively, it is also possible to employ a configuration where a higher-order control apparatus designates linear interpolation or non-linear interpolation.

0093Further, the gain encoding circuit 23 encodes a sample length T[k], a gain value g[k] and a gain inclination value s[k] indicating the sample position as appropriate for each gain sample position to obtain gain information. It should be noted that, when the interpolation mode information is information indicating an interpolation scheme using linear interpolation, gain information only including the sample length and the gain value and not including the gain inclination value is generated.

0094The gain encoding circuit 23 supplies the gain code string including the gain information of each gain sample position and the interpolation mode information obtained in this manner to the multiplexing circuit 25.

0095In step S14, the signal encoding circuit 24 encodes the supplied input time series signal according to a predetermined encoding scheme and supplies the signal code string obtained as a result of encoding to the multiplexing circuit 25.

0096In step S15, the multiplexing circuit 25 multiplexes the gain code string supplied from the gain encoding circuit 23 and the signal code string supplied from the signal encoding circuit 24 and outputs the output code string obtained as a result of multiplexing. When the output code string corresponding to one frame is outputted as a bit stream in this manner, encoding processing ends. Then, encoding processing of the next frame is performed.

0097As described above, the encoding apparatus 11 obtains the gain value for each sample within a frame of the input time series signal to extract the gain sample position and generates the gain code string constituted with gain information of each gain sample position and interpolation mode information.

0098By the gain value for each sample within a frame being determined in this manner, at the decoding side, temporal waveforms between frames of the audio signal are smoothly connected, so that it is possible to obtain sound with higher quality. Moreover, by the interpolation mode information being included in the gain code string, it is possible to reproduce a gain waveform with high precision with a less code amount by utilizing non-linear interpolation as appropriate.

<Configuration Example of Decoding Apparatus>

0099A decoding apparatus which receives the output code string outputted from the encoding apparatus 11 as an input code string and decodes the input code string will be described next.

0100<figref idref="f0006">FIG. 7</figref> is a diagram illustrating a configuration example of an embodiment of the decoding apparatus to which the present technology is applied.

0101The decoding apparatus 51 illustrated in <figref idref="f0006">FIG. 7</figref> has a demultiplexing circuit 61, a signal decoding circuit 62, a gain decoding circuit 63 and a gain applying circuit 64.

0102The demultiplexing circuit 61 demultiplexes the supplied input code string, that is, the output code string received from the encoding apparatus 11 and supplies the signal code string obtained as a result of demultiplexing to the signal decoding circuit 62, while supplying the gain code string to the gain decoding circuit 63.

0103The signal decoding circuit 62 decodes the signal code string supplied from the demultiplexing circuit 61 and supplies a time series signal obtained as a result of decoding to the gain applying circuit 64. Here, the time series signal is, for example, an audio signal of 11.1 ch or 7.1 ch, and an audio signal of channels constituting the time series signal is set as a pulse code modulation (PCM) signal.

0104The gain decoding circuit 63 decodes the gain code string supplied from the demultiplexing circuit 61 and supplies a gain value obtained as a result of decoding to the gain applying circuit 64. The gain decoding circuit 63 has an interpolation processing unit 71, which calculates a gain value at each sample position of the time series signal through linear interpolation or non-linear interpolation based on the gain information and the interpolation mode information obtained from the gain code string.

0105The gain applying circuit 64 corrects volume of the time series signal by adjusting a gain of the time series signal supplied from the signal decoding circuit 62 based on the gain value supplied from the gain decoding circuit 63 and outputs an output time series signal obtained as a result of volume correction.

<Explanation of Decoding Processing>

0106Subsequently, operation of the decoding apparatus 51 will be described.

0107When the input code string corresponding to one frame is supplied, the decoding apparatus 51 performs decoding processing of decoding the input code string and outputting an output time series signal. The decoding processing by the decoding apparatus 51 will be described below with reference to the flowchart of <figref idref="f0007">FIG. 8</figref>.

0108In step S41, the demultiplexing circuit 61 receives the input code string transmitted from the encoding apparatus 11 and demultiplexes the input code string, and supplies a signal code string obtained as a result of demultiplexing to the signal decoding circuit 62, while supplying the gain code string to the gain decoding circuit 63.

0109In step S42, the signal decoding circuit 62 decodes the signal code string supplied from the demultiplexing circuit 61 and supplies a time series signal obtained as a result of decoding to the gain applying circuit 64.

0110In step S43, the gain decoding circuit 63 performs gain decoding processing to decode the gain code string supplied from the demultiplexing circuit 61 and supplies a gain value at each sample position of a frame to be processed obtained as a result of decoding to the gain applying circuit 64. It should be noted that details of the gain decoding processing will be described later.

0111In step S44, the gain applying circuit 64 adjusts a gain of the time series signal supplied from the signal decoding circuit 62 based on the gain value supplied from the gain decoding circuit 63 and outputs the obtained output time series signal. That is, each sample of the time series signal is multiplied by the gain value to be made an output time series signal with appropriate volume.

0112When the output time series signal is outputted, the decoding processing ends.

0113As described above, the decoding apparatus 51 decodes the gain code string, and applies the obtained gain value at each sample position to the time series signal to adjust a gain (volume) in a time domain. By adjusting a gain with a gain value determined for each sample position in this manner, it is possible to smoothly connect time waveforms between frames of the output time series signal, so that it is possible to obtain sound with higher quality.

0114Moreover, because a gain waveform is obtained by utilizing non-linear interpolation as appropriate, even when the gain waveform is a smooth waveform, it is possible to reproduce the gain waveform with high precision with a less code amount.

<Explanation of Gain Decoding Processing>

0115Further, gain decoding processing corresponding to processing in step S43 of <figref idref="f0007">FIG. 8</figref> will be described with reference to the flowchart of <figref idref="f0008">FIG. 9</figref>.

0116In step S71, the gain decoding circuit 63 reads out gain information at a gain sample position to be processed from the gain code string supplied from the demultiplexing circuit 61 and decodes a sample length T[k], a gain value g[k] and a gain inclination value s[k] included as the gain information as necessary. It should be noted that when an interpolation scheme indicated by the interpolation mode information is an interpolation scheme using linear interpolation, the gain inclination value is not included in the gain information.

0117For example, in the gain code string, gain information and interpolation mode information at each gain sample position are stored while being arranged in ascending order of a distance from the head of the frame. Because the gain decoding circuit 63 sequentially reads out the gain information and the interpolation mode information from the gain code string, a gain sample position is set as a gain sample position to be processed in ascending order of a distance from the head of the frame.

0118In step S72, the gain decoding circuit 63 reads out the interpolation mode information at the gain sample position to be processed from the gain code string.

0119It should be noted that while an example where the interpolation mode information is included in the gain code string will be described here, the interpolation mode information may be included in a header, or the like, of a bit stream in which an input code string of each frame is included, or the interpolation mode information may be acquired from a higher-order control apparatus, or the like.

0120In step S73, the interpolation processing unit 71 determines whether or not the interpolation scheme indicated by the read-out interpolation mode information is a scheme using linear interpolation.

0121In step S73, when it is determined that the interpolation scheme is a scheme using linear interpolation, in step S74, the interpolation processing unit 71 performs linear interpolation to generate a gain waveform.

0122Specifically, the interpolation processing unit 71 performs the same calculation as that of the above-described equation (1) based on the gain value g[k] and the sample length T[k-1] at the gain sample position to be processed, and a gain value and a sample position at a gain sample position one position closer to the head of the frame from the gain sample position to be processed to generate a gain waveform between the gain sample positions. That is, a gain value at each sample position located between two gain sample positions of the time series signal is calculated, and a waveform constituted with gain values at the sample positions is set as a gain waveform.

0123When the gain waveform between two adjacent gain sample positons is obtained in this manner, the processing proceeds to step S76.

0124On the other hand, when it is determined in step S73 that the scheme is a scheme which does not use linear interpolation, that is, a scheme using non-linear interpolation, in step S75, the interpolation processing unit 71 performs non-linear interpolation to generate a gain waveform.

0125Specifically, the interpolation processing unit 71 performs the same calculation as that of the above-described equation (4) based on the gain value g[k], the sample length T[k-1] and the gain inclination value s[k] at the gain sample position to be processed and a gain value, a sample position and a gain inclination value at a gain sample position one position closer to the head of the frame from the gain sample position to be processed to generate a gain waveform between the gain sample positions. That is, a gain value at each sample position located between two gain sample positions of the time series signal is calculated, and a waveform constituted with gain values of the sample positions is set as a gain waveform.

0126When the gain waveform between two adjacent gain sample positions is obtained in this manner, the processing proceeds to step S76.

0127When the gain waveform between the gain sample positons is obtained through interpolation in step S74 or step S75, in step S76, the gain decoding circuit 63 determines whether or not processing is performed for all the gain sample positions.

0128When it is determined in step S76 that not all of the gain sample positions are processed yet, the processing returns to step S71, and the above-described processing is repeated. That is, the next gain sample position is selected as a processing target, and a gain waveform is obtained through interpolation.

0129On the other hand, when it is determined in step S76 that all of the gain sample positions are processed, the gain decoding circuit 63 supplies a gain waveform corresponding to one frame constituted with gain values at the sample positions obtained through the processing so far to the gain applying circuit 64, and the gain decoding processing ends. When the gain decoding processing ends, then, the processing proceeds to step S44 in <figref idref="f0007">FIG. 8</figref>.

0130The decoding apparatus 51 obtains a gain waveform through linear interpolation or non-linear interpolation according to the interpolation mode information as described above. By obtaining a gain waveform through non-linear interpolation as appropriate according to the interpolation mode information in this manner, it is possible to reproduce a gain waveform with high precision with a less code amount.

0131It should be noted that while an example has been described above where the interpolation mode information is generated for each gain sample position, and the interpolation scheme is switched between linear interpolation and non-linear interpolation, one piece of the interpolation mode information may be generated for each frame. In this case, the interpolation scheme is switched between linear interpolation and non-linear interpolation in units of a frame.

0132Further, the interpolation scheme may be switched between linear interpolation and non-linear interpolation in units of a plurality of frames or in units of a file. For example, when the interpolation scheme is switched in units of a file, for example, one piece of interpolation mode information is stored in a header of the bit stream. The interpolation processing unit 71 performs interpolation processing of each frame using an interpolation scheme indicated by the interpolation mode information, that is, either the scheme using linear interpolation or the scheme using non-linear interpolation to obtain a gain waveform corresponding to one file.

<Second Embodiment>

<Limiting>

0133By the way, the gain waveform obtained through non-linear interpolation is different from the gain waveform obtained through linear interpolation, and there is a case where a gain value at a sample position between two gain sample positions may be greater or smaller than gain values at two gain sample positions included in the gain code string.

0134For example, in the example illustrated in <figref idref="f0002">FIG. 3</figref>, in part of the gain waveform indicated with the curve C21, which is obtained through non-linear interpolation, there is a portion where the gain value becomes smaller than the gain value g[k] at the gain sample position G11. Further, in part of the gain waveform indicated with the curve C21, there is also a portion where the gain value becomes greater than the gain value g[k+1] at the gain sample position G12.

0135Therefore, there is a case where the gain value obtained through non-linear interpolation becomes a negative (minus) value which is inappropriate as the gain value. Therefore, in order to prevent the gain value obtained through interpolation from becoming an inappropriate value, it is also possible to perform limiting on the gain value using zero as a lower limit by performing calculation of the following equation (11). [Math. 11] <maths id="math0011" num="(11)"><math display="block"><mi mathvariant="normal">g</mi><mo>_</mo><mi>interpolated</mi><mfenced open="[" close="]"><mi mathvariant="normal">n</mi></mfenced><mo>=</mo><mi>max</mi><mfenced><mn>0</mn><mo>,</mo><mi mathvariant="normal">g</mi><mo>_</mo><mi>interpolated</mi><mfenced open="[" close="]"><mi mathvariant="normal">n</mi></mfenced></mfenced></math><img file="EP3608909B1_D0011.tif" /></maths>

0136In equation (11), between the gain value g_interpolated[n] obtained through interpolation and zero, a greater one is made a final gain value g_interoplated[n]. Accordingly, the final gain value is equal to or greater than zero, and the gain value does not become a negative value.

0137Further, there is a case where it is desired to boost (amplify) the time series signal and a case where it is desired to compress (suppress) the time series signal through gain adjustment (volume correction).

0138For example, when it is desired to boost the time series signal, if the gain value is smaller than one, the gain value becomes an inappropriate value. Therefore, when the time series signal is boosted, it is also possible to perform limiting on the gain value using one as a lower limit by performing calculation of the following equation (12). [Math. 12] <maths id="math0012" num="(12)"><math display="block"><mi mathvariant="normal">g</mi><mo>_</mo><mi>interpolated</mi><mfenced open="[" close="]"><mi mathvariant="normal">n</mi></mfenced><mo>=</mo><mi>max</mi><mfenced><mn>1</mn><mo>,</mo><mi mathvariant="normal">g</mi><mo>_</mo><mi>interpolated</mi><mfenced open="[" close="]"><mi mathvariant="normal">n</mi></mfenced></mfenced></math><img file="EP3608909B1_D0012.tif" /></maths>

0139In equation (12), between the gain value g_interpolated[n] obtained through interpolation and one, a greater one is made a final gain value g_interpolated[n]. Accordingly, the gain value does not become a value less than one. In other words, the gain value is always equal to or greater than one which is the lower limit.

0140Further, for example, when it is desired to compress the time series signal, if the gain value is greater than one, the gain value becomes an inappropriate value. Therefore, when the time series signal is compressed, it is also possible to perform limiting on the gain value using one as an upper limit by performing calculation of the following equation (13). [Math. 13] <maths id="math0013" num="(13)"><math display="block"><mi mathvariant="normal">g</mi><mo>_</mo><mi>interpolated</mi><mfenced open="[" close="]"><mi mathvariant="normal">n</mi></mfenced><mo>=</mo><mi>min</mi><mfenced><mn>1</mn><mo>,</mo><mi mathvariant="normal">g</mi><mo>_</mo><mi>interpolated</mi><mfenced open="[" close="]"><mi mathvariant="normal">n</mi></mfenced></mfenced></math><img file="EP3608909B1_D0013.tif" /></maths>

0141In equation (13), between the gain value g_interpolated[n] obtained through interpolation and one, a smaller one is made a final gain value g_interpolated[n]. Accordingly, the gain value does not become a value greater than one. In other words, the gain value is always equal to or smaller than one which is the upper limit.

0142When limiting processing as indicated in equation (12) or equation (13) is performed, it is only necessary to provide limiting information indicating whether the gain waveform is used for boosting or used for compression to the gain decoding circuit 63 as information regarding the encoded gain waveform. For example, the limiting information may be supplied from a higher-order control apparatus to the gain decoding circuit 63, or the limiting information may be included in the gain code string, the header of the bit stream, or the like.

0143In the following, description will be continued assuming that the limiting information is included in the gain code string. In this case, in the processing of step S13 in <figref idref="f0013">FIG. 15</figref>, the gain code string including the limiting information is generated.

0144By performing the limiting processing on the gain value as described above, it is possible to obtain a more appropriate gain value. By this means, it is possible to perform more appropriate gain adjustment (volume control), and, as a result, it is possible to obtain sound with higher quality.

<Configuration Example of Decoding Apparatus>

0145When limiting processing is performed on the gain value, the decoding apparatus 51 is configured as illustrated in, for example, <figref idref="f0009">FIG. 10</figref>. It should be noted that, in <figref idref="f0009">FIG. 10</figref>, the same reference numerals as those in <figref idref="f0006">FIG. 7</figref> are assigned to portions corresponding to those in <figref idref="f0006">FIG. 7</figref>, and explanation thereof will be omitted as appropriate.

0146The decoding apparatus 51 illustrated in <figref idref="f0009">FIG. 10</figref> has a different configuration from that of the decoding apparatus 51 in <figref idref="f0006">FIG. 7</figref> in that a limiting processing unit 101 is newly provided at the gain decoding circuit 63, and has the same configuration as that of the decoding apparatus 51 in <figref idref="f0006">FIG. 7</figref> in other points.

0147The limiting processing unit 101 performs limiting processing on the gain value calculated through non-linear interpolation performed by the interpolation processing unit 71 to obtain a final gain value.

<Explanation of Gain Decoding Processing>

0148Gain decoding processing performed in the case where the decoding apparatus 51 has the configuration illustrated in <figref idref="f0009">FIG. 10</figref> will be described next.

0149For example, at the decoding apparatus 51, the decoding processing described with reference to <figref idref="f0007">FIG. 8</figref> is performed. However, in gain decoding processing corresponding to step S43, the gain decoding processing illustrated in <figref idref="f0010">FIG. 11</figref> is performed. The gain decoding processing by the decoding apparatus 51 in <figref idref="f0009">FIG. 10</figref> will be described below with reference to the flowchart of <figref idref="f0010">FIG. 11</figref>.

0150It should be noted that the processing from step S101 to step S105 is the same as processing from step S71 to step S75 in <figref idref="f0008">FIG. 9</figref>, explanation thereof will be omitted.

0151In step S106, the limiting processing unit 101 changes the gain value as appropriate so that the gain value does not become a negative value by performing calculation of the above-described equation (11) on the gain value at each sample position obtained through processing in step S105.

0152Further, the limiting processing unit 101 obtains a final gain value by further performing calculation of either equation (12) or equation (13) on the gain value limited through calculation of equation (11) according to the limiting information included in the gain code string.

0153Specifically, when the limiting information included in the gain code string indicates that the gain waveform is to be used for boosting, the limiting processing unit 101 performs calculation of equation (12) so that the gain value does not become a value less than one.

0154On the other hand, when the limiting information included in the gain code string indicates that the gain waveform is to be used for compression, the limiting processing unit 101 performs calculation of equation (13) so that the gain value does not become a value greater than one.

0155When the gain waveform is generated through linear interpolation in step S104 or limiting processing is performed in step S106, the processing in step S107 is performed, and the gain decoding processing ends. Because the processing in step S107 is the same as the processing in step S76 in <figref idref="f0008">FIG. 9</figref>, explanation thereof will be omitted.

0156As described above, the decoding apparatus 51 performs limiting processing on the gain value obtained through non-linear interpolation. By this means, it is possible to perform gain adjustment (volume correction) with a more appropriate gain value. It is therefore possible to obtain sound with higher quality.

<Third Embodiment>

<Interpolation of Gain Value>

0157Further, while, in the above description, an example has been described where the gain waveform is obtained while the interpolation scheme for interpolating the gain value is switched between linear interpolation and non-linear interpolation for each gain sample position, it is also possible to employ a configuration where non-linear interpolation is basically performed, and linear interpolation is performed only under specific conditions.

0158For example, a case will be studied where the gain waveform indicated with a broken line L41 illustrated in <figref idref="f0011">FIG. 12</figref> is encoded, and the gain waveform is obtained at the decoding side through non-linear interpolation. It should be noted that <figref idref="f0011">FIG. 12</figref> indicates a gain value on a vertical axis and a sample position on a horizontal axis.

0159It is assumed that, at the encoding apparatus 11, the k-th gain sample position G21 and the k+1-th gain sample position G22 are extracted, and the gain code string including gain values, sample lengths and gain inclination values at these gain sample positions is obtained.

0160Here, an arrow D21 indicates a gain inclination value s[k] at the gain sample position G21, and an arrow D22 indicates a gain inclination value s[k+1] at the gain sample position G22.

0161It is now assumed that non-linear interpolation using a cubic function is performed at the decoding apparatus 51 based on the gain values, the sample lengths and the gain inclination values included in the gain code string, and a gain waveform indicated with a curve C31 is obtained.

0162In this example, a difference between the gain waveform indicated with the curve C31 obtained through non-linear interpolation and the gain waveform indicated with a broken line L41 becomes large.

0163In a scheme for obtaining a gain waveform through non-linear interpolation, when a gain waveform whose gain value linearly changes is encoded as with this example, a difference between the original gain waveform and a gain waveform obtained through non-linear interpolation upon decoding becomes large.

0164To make this difference small, it is necessary to perform processing (local decoding) of adjusting a gain value and a gain inclination value to be encoded at the encoding apparatus 11 by calculating the gain waveform obtained through non-linear interpolation, which increases a processing amount of encoding.

0165Therefore, in the present technology, when non-linear interpolation is performed at the decoding apparatus 51, by allowing linear interpolation to be performed under specific conditions, a gain waveform is reproduced with high precision with a less processing amount of encoding.

0166Specifically, when, for example, a gain value at a sample position between the k-th gain sample position and the k+1-th gain sample position is obtained through interpolation, an intersection X[k, k+1] of two straight line 1[k] and straight line 1[k+1] is obtained from gain values and gain inclination values at these gain sample positions.

0167Here, the straight line 1[k] is a straight line which passes through the k-th gain sample position (point) on the gain waveform and which has inclination indicated with the gain inclination value s[k]. That is, when a value of the coordinate in the sample axis direction is the same as a value of the k-th gain sample position, the straight line 1[k] is a straight line which has a gain value g[k] at the k-th gain sample position as the value of the coordinate in the gain axis direction and which has inclination indicated with the gain inclination value s[k].

0168In a similar manner, the straight line 1[k+1] is a straight line which passes through the k+1-th gain sample position and which has inclination indicated with the gain inclination value s[k+1].

0169Further, it is determined whether or not a distance between either the k-th gain sample position or the k+1-th gain sample position and the obtained intersection X[k, k+1] is equal to or less than a predetermined threshold. In the determination here, it is determined whether, for example, the following equation (14) holds true. [Math. 14] <maths id="math0014" num="(14)"><math display="block"><mrow><mfenced><mfenced><mi mathvariant="normal">d</mi><mo>_</mo><mi>sample</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>≤</mo><mi>thre</mi><mo>_</mo><mi>sample</mi></mfenced><mo>&amp;</mo><mo>&amp;</mo><mfenced><mi mathvariant="normal">d</mi><mo>_</mo><mi>gain</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>≤</mo><mi>thre</mi><mo>_</mo><mi>gain</mi></mfenced></mfenced><mo>‖</mo></mrow><mfenced><mfenced><mi mathvariant="normal">d</mi><mo>_</mo><mi>sample</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>≤</mo><mi>thre</mi><mo>_</mo><mi>sample</mi></mfenced><mo>&amp;</mo><mo>&amp;</mo><mfenced><mi mathvariant="normal">d</mi><mo>_</mo><mi>gain</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>≤</mo><mi>thre</mi><mo>_</mo><mi>gain</mi></mfenced></mfenced></math><img file="EP3608909B1_D0014.tif" /></maths>

0170It should be noted that, in equation (14), d_sample[k] and d_sample[k+1] respectively indicate distances from the k-th gain sample position and the k+1-th gain sample position to the intersection X[k, k+1] in the sample axis direction. Further, d_gain[k] and d_gain[k+1] respectively indicate distances from the k-th gain sample position and the k+1-th gain sample position to the intersection X[k, k+1] in the gain axis direction, that is, differences of the gain values.

0171Further, thre_sample and thre_gain respectively indicate a threshold of a distance in the sample axis direction and a threshold of a distance in the gain axis direction.

0172Therefore, in equation (14), when the distance d_sample[k] is equal to or less than thre_sample, and the distance d_gain[k] is equal to or less than thre_gain, or when the distance d_sample[k+1] is equal to or less than thre_sample and the distance d_gain[k+1] is equal to or less than the threshold thre_gain, a distance from the gain sample position to the intersection X[k, k+1] is equal to or less than a threshold.

0173For example, when the k-th gain sample position is a head position of the frame, that is, a sample position of n = 0, the distance d_sample[k], the distance d_gain[k], the distance d_sample[k+1] and the distance d_gain[k+1] in equation (14) are respectively obtained using the following equation (15) to equation (18). Further, the threshold thre_sample and the threshold thre_gain are, for example, the threshold thre_sample = 32 and the threshold thre_gain = 0.01. [Math. 15] <maths id="math0015" num="(15)"><math display="block"><mi mathvariant="normal">d</mi><mo>_</mo><mi>sample</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mi>abs</mi><mfenced><mfenced><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>×</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>/</mo><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced></mfenced></mfenced></math><img file="EP3608909B1_D0015.tif" /></maths> [Math. 16] <maths id="math0016" num="(16)"><math display="block"><mi mathvariant="normal">d</mi><mo>_</mo><mi>gain</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mi>abs</mi><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>×</mo><mfenced><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>×</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>/</mo><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced></mfenced></mfenced></math><img file="EP3608909B1_D0016.tif" /></maths> [Math. 17] <maths id="math0017" num="(17)"><math display="block"><mi mathvariant="normal">d</mi><mo>_</mo><mi>sample</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>=</mo><mi>abs</mi><mfenced><mfenced><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>×</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>/</mo><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced></mfenced><mo>−</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced></math><img file="EP3608909B1_D0017.tif" /></maths> [Math. 18] <maths id="math0018" num="(18)"><math display="block"><mi mathvariant="normal">d</mi><mo>_</mo><mi>gain</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>=</mo><mi>abs</mi><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>×</mo><mfenced><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>×</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>/</mo><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced></mfenced><mo>+</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced></mfenced></math><img file="EP3608909B1_D0018.tif" /></maths>

0174It should be noted that, in equation (15) to equation (18), abs(x) indicates that an absolute value of x is obtained.

0175When it is determined that such a conditional expression indicated with equation (14) holds true, a gain waveform is obtained through linear interpolation, that is, through calculation of the above-described equation (1). On the other hand, when the conditional expression indicated with equation (14) does not hold true, a gain waveform is obtained through non-linear interpolation, that is, through calculation of the above-described equation (4).

0176For example, as illustrated in <figref idref="f0011">FIG. 13</figref>, when a gain value at each sample position between the gain sample position G31 and the gain sample position G32 is obtained through interpolation, whether or not the conditional expression indicated with equation (14) holds true is determined by specifying which of a region TR11 and a region TR12 the intersection CP11 is included in. It should be noted that <figref idref="f0011">FIG. 13</figref> indicates a gain value on a vertical axis and a sample position within a frame of the time series signal on a horizontal axis.

0177In <figref idref="f0011">FIG. 13</figref>, the gain sample position G31 indicates the k-th gain sample position, and the arrow D31 indicates the gain inclination value s[k] at the gain sample position G31. Therefore, the straight line L51 is a straight line 1[k].

0178In a similar manner, the gain sample position G32 indicates the k+1-th gain sample position, and the arrow D32 indicates the gain inclination value s[k+1] at the gain sample position G32. Therefore, the straight line L52 is a straight line 1[k+1]. The intersection CP11 which is an intersection of the straight line L51 and the straight line L52 is an intersection X[k, k+1].

0179It is now assumed that the region TR11 has the gain sample position G31 in the center and has a length in a vertical direction of 2 × thre_gain, and a length in a horizontal direction of 2 × thre_sample in the drawing. In a similar manner, it is assumed that the region TR12 has the gain sample position G21 in the center and, has a length in a vertical direction of 2 × thre_gain and a length in a horizontal direction of 2 × thre_sample in the drawing.

0180In this case, when the intersection CP11 is located within the region TR11 or the intersection CP11 is located within the region TR12, the conditional expression indicated with equation (14) holds true. In the example of <figref idref="f0011">FIG. 13</figref>, because the intersection CP11 is located within the region TR12, the conditional expression indicated with equation (14) holds true.

0181In the example illustrated in <figref idref="f0011">FIG. 13</figref>, the original gain waveform to be reproduced (restored) should have been a waveform close to a waveform constituted with the straight line L51 and the straight line L52. That is, in more detail, the waveform should have been close to the straight line L51 from the gain sample position G31 to the intersection CP11, and should have been close to the straight line L52 from the intersection CP11 to the gain sample position G32.

0182However, because, in this example, the intersection CP11 is located within the region TR12, and a distance between the intersection CP11 to the gain sample position G32 is sufficiently short, it is possible to determine that the original gain waveform is approximated as a straight line connecting the gain sample position G31 and the gain sample position G32.

0183In this case, because at the gain waveform between the gain sample position G31 and the gain sample position G32, the gain value can substantially linearly change, it is possible to reproduce the gain waveform with higher precision by obtaining the gain waveform through linear interpolation rather than obtaining the gain waveform through non-linear interpolation. Therefore, in the present technology, when the conditional expression indicated with the above-described equation (14) holds true, the gain waveform is obtained through linear interpolation.

0184Accordingly, in the example of <figref idref="f0011">FIG. 13</figref>, a gain value at each sample position between the gain sample position G31 and the gain sample position G32 is obtained through linear interpolation, and, by this means, for example, a gain waveform illustrated in <figref idref="f0012">FIG. 14</figref> can be obtained. It should be noted that, in <figref idref="f0012">FIG. 14</figref>, the same reference numerals as those in <figref idref="f0011">FIG. 13</figref> are assigned to portions corresponding to those in <figref idref="f0011">FIG. 13</figref>, and explanation thereof will be omitted as appropriate.

0185In <figref idref="f0012">FIG. 14</figref>, a straight line L61 connecting the gain sample position G31 and the gain sample position G32 is obtained as a gain waveform between the gain sample position G31 and the gain sample position G32.

0186Further, for example, also in the above-described example illustrated in <figref idref="f0011">FIG. 12</figref>, because the conditional expression indicated with equation (14) holds true, the gain waveform is obtained through linear interpolation.

0187In the example of <figref idref="f0011">FIG. 12</figref>, because the intersection X[k, k+1] is located at the gain sample position G22, equation (14) holds true, and a straight line connecting the gain sample position G21 and the gain sample position G22 is set as a gain waveform between the gain sample positions. Therefore, in this example, the original gain waveform is accurately reproduced.

0188As described above, when non-linear interpolation is basically performed while linear interpolation is performed under specific conditions, it is possible to make a difference between the original gain waveform and the decoded gain waveform smaller without increasing a processing amount of encoding.

0189Moreover, by employing such a decoding scheme, because both linear interpolation and non-linear interpolation can be performed only with a scheme in which non-linear interpolation is performed, it becomes unnecessary to include the interpolation mode information in the gain code string, so that it is possible to lower a bit rate of the output code string. That is, it is possible to reduce a code amount of the output code string.

<Configuration Example of Decoding Apparatus>

0190When linear interpolation is performed under specific conditions, the decoding apparatus 51 is configured as illustrated in, for example, <figref idref="f0013">FIG. 15</figref>. It should be noted that, in <figref idref="f0013">FIG. 15</figref>, the same reference numerals as those in <figref idref="f0006">FIG. 7</figref> are assigned to portions corresponding to those in <figref idref="f0006">FIG. 7</figref>, and explanation thereof will be omitted as appropriate.

0191The decoding apparatus 51 illustrated in <figref idref="f0013">FIG. 15</figref> has a different configuration from that of the decoding apparatus 51 in <figref idref="f0006">FIG. 7</figref> in that an operation unit 131 is newly provided at the gain decoding circuit 63 and has the same configuration as that of the decoding apparatus 51 in <figref idref="f0006">FIG. 7</figref> in other points.

0192The operation unit 131 performs calculation of the above-described conditional expression indicated with equation (14).

<Explanation of Gain Decoding Processing>

0193The gain decoding processing performed when the decoding apparatus 51 is configured as illustrated in <figref idref="f0013">FIG. 15</figref> will be described next.

0194For example, while, at the encoding apparatus 11, the encoding processing described with reference to <figref idref="f0004">FIG. 5</figref> is performed, in the gain encoding processing in step S13, the gain code string only including the gain information and not including the interpolation mode information is generated, and the output code string obtained through multiplexing is outputted. Further, in this case, the gain information always includes the gain inclination value.

0195At the decoding apparatus 51, the decoding processing described with reference to <figref idref="f0007">FIG. 8</figref> is performed. However, in the gain decoding processing corresponding to step S43, the gain decoding processing illustrated in <figref idref="f0014">FIG. 16</figref> is performed. The gain decoding processing by the decoding apparatus 51 in <figref idref="f0013">FIG. 15</figref> will be described below with reference to the flowchart of <figref idref="f0014">FIG. 16</figref>.

0196It should be noted that because processing in step S131 is the same as the processing in step S71 in <figref idref="f0008">FIG. 9</figref>, explanation thereof will be omitted.

0197In step S132, the operation unit 131 calculates the conditional expression indicated with equation (14) based on the read-out gain information.

0198That is, the operation unit 131 performs the same calculation as the above-described equation (15) to equation (18) based on the gain value, the sample length and the gain inclination value at the gain sample position read out as the gain information. The operation unit 131 then performs calculation of equation (14) based on a distance from the gain sample position obtained as a result of the calculation to the intersection X[k, k+1].

0199This calculation of equation (15) to equation (18) is equivalent to obtaining the straight line 1[k] and the straight line 1[k+1] and obtaining the intersection X[k, k+1] of these straight lines and, further, obtaining differences between the gain values at the k-th gain sample position and the k+1-th gain sample position and the gain value at the intersection X[k, k+1]. Further, calculation of the conditional expression of equation (14) is equivalent to determining whether or not the differences between the gain values at the gain sample positions and the gain value at the intersection X[k, k+1] are equal to or less than a predetermined threshold.

0200Therefore, at the decoding apparatus 51, it is possible to obtain a gain value at each sample position between the two gain sample positions through linear interpolation or non-linear interpolation according to the differences between the gain values at the gain sample positions and the gain value at the intersection X[k, k+1].

0201In step S133, the interpolation processing unit 71 determines whether or not linear interpolation is performed based on a calculation result of the conditional expression in step S132. For example, when the conditional expression indicated with equation (14) holds true, it is determined that linear interpolation is performed.

0202When it is determined in step S133 that linear interpolation is performed, in step S134, the interpolation processing unit 71 performs linear interpolation to generate a gain waveform, and, then, the processing proceeds to step S136. In step S134, the same processing as the processing in step S74 in <figref idref="f0008">FIG. 9</figref> is performed.

0203On the other hand, when it is determined in step S133 that linear interpolation is not performed, in step S135, the interpolation processing unit 71 performs non-linear interpolation to generate a gain waveform, and, then, the processing proceeds to step S136. It should be noted that, in step S135, the same processing as the processing in step S75 in <figref idref="f0008">FIG. 9</figref> is performed.

0204When the gain waveform is generated in step S134 or step S135, the processing in step S136 is performed, and the gain decoding processing ends. Because the processing in step S136 is the same as the processing in step S76 in <figref idref="f0008">FIG. 9</figref>, explanation thereof will be omitted.

0205As described above, the decoding apparatus 51 generates a gain waveform through linear interpolation under specific conditions. By this means, it is possible to obtain the original gain waveform with higher precision with a less processing amount and it is possible to reduce a code amount of the output code string.

<Modified Example 1 of Third Embodiment>

<Interpolation of Gain Value>

0206It should be noted that, while, in the third embodiment, a case has been described where linear interpolation is performed under specific conditions, it is also possible to perform linear interpolation on the gain value by utilizing the gain sample positions and the intersection.

0207That is, in the third embodiment, a gain value at each sample position between two gain sample positions is calculated through linear interpolation using equation (1). In the present embodiment, instead, a waveform constituted with straight lines respectively connecting the intersection CP11 of the two straight line L51 and straight line L52 as illustrated in <figref idref="f0015">FIG. 17</figref> and two gain sample positions is set as a gain waveform obtained through linear interpolation. It should be noted that, in <figref idref="f0015">FIG. 17</figref>, the same reference numerals as those in <figref idref="f0011">FIG. 13</figref> are assigned to portions corresponding to those in <figref idref="f0011">FIG. 13</figref>, and explanation thereof will be omitted as appropriate.

0208In this example, a broken line L71 constituted with a straight line connecting the gain sample position G31 and the intersection CP11 and a straight line connecting the gain sample position G32 and the intersection CP11 is set as a gain waveform between the gain sample position G31 and the gain sample position G32.

0209In the example of the gain waveform illustrated in <figref idref="f0015">FIG. 17</figref>, when linear interpolation is performed with the straight line connecting the two gain sample positions, in order to reproduce the gain waveform more accurately, it is necessary to set three or more gain sample positions in a section between the gain sample position G31 and the gain sample position G32 upon encoding of the gain waveform.

0210That is, if sample positions of the gain sample position G31, the intersection CP11 and the gain sample position G32 are set as the gain sample positions upon encoding of the gain waveform, a difference (error) occurs between the gain waveform before encoded and the gain waveform obtained through decoding.

0211On the other hand, when the broken line L71 is set as the gain waveform by utilizing the intersection CP11, by only setting two positions of the gain sample position G31 and the gain sample position G32 as the gain sample positions, it is possible to make a difference between the gain waveform before encoded and the gain waveform obtained through decoding smaller. Therefore, in a method in which linear interpolation is performed while utilizing the intersection, it is possible to reduce the number of gain sample positions, and thereby it is possible to suppress a bit rate of the output code string and improve coding efficiency.

0212It should be noted that, when linear interpolation is performed while utilizing the intersection, the intersection of the two straight lines has to be located between the two gain sample positions.

0213For example, in the example of <figref idref="f0015">FIG. 17</figref>, the intersection CP11 has to be located between the gain sample position G31 and the gain sample position G32 in the sample axis direction.

0214Therefore, a region used for determining whether non-linear interpolation is performed or linear interpolation is performed is different between the example in <figref idref="f0011">FIG. 13</figref> and the example in <figref idref="f0015">FIG. 17</figref>. In the example in <figref idref="f0015">FIG. 17</figref>, when the intersection CP11 is included in either the region TR21 or the region TR22, linear interpolation utilizing the intersection is performed.

0215Here, the region TR21 is a right half region of the region TR11 illustrated in <figref idref="f0011">FIG. 13</figref>, that is, a region at the right side of the region TR11 with respect to the gain sample position G31 in <figref idref="f0011">FIG. 13</figref>. In a similar manner, the region TR22 is a left half region of the region TR12 illustrated in <figref idref="f0011">FIG. 13</figref>, that is, a region at the left side of the region TR12 with respect to the gain sample position G32 in <figref idref="f0011">FIG. 13</figref>.

0216In this manner, when linear interpolation utilizing the intersection is performed, the conditional expression corresponding to equation (14) is as indicated with the following equation (19). That is, when the following equation (19) holds true, linear interpolation utilizing the intersection is performed. [Math. 19] <maths id="math0019" num="(19)"><math display="block"><mrow><mfenced><mfenced><mn>0</mn><mo>&lt;</mo><mi mathvariant="normal">d</mi><mo>_</mo><mi>sample</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>&amp;</mo><mo>&amp;</mo><mfenced><mi mathvariant="normal">d</mi><mo>_</mo><mi>sample</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>≤</mo><mi>thre</mi><mo>_</mo><mi>sample</mi></mfenced><mo>&amp;</mo><mo>&amp;</mo><mfenced><mi mathvariant="normal">d</mi><mo>_</mo><mi>gain</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>≤</mo><mi>thre</mi><mo>_</mo><mi>gain</mi></mfenced></mfenced><mo>‖</mo></mrow><mfenced><mfenced><mn>0</mn><mo>&lt;</mo><mi mathvariant="normal">d</mi><mo>_</mo><mi>sample</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced></mfenced><mo>&amp;</mo><mo>&amp;</mo><mfenced><mi mathvariant="normal">d</mi><mo>_</mo><mi>sample</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>≤</mo><mi>thre</mi><mo>_</mo><mi>sample</mi></mfenced><mo>&amp;</mo><mo>&amp;</mo><mfenced><mi mathvariant="normal">d</mi><mo>_</mo><mi>gain</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>≤</mo><mi>thre</mi><mo>_</mo><mi>gain</mi></mfenced></mfenced></math><img file="EP3608909B1_D0019.tif" /></maths>

0217In equation (19), when the distance d_sample[k] is greater than zero, and equal to or less than thre_sample, and the distance d_gain[k] is equal to or less than the threshold thre_gain, or when the distance d_sample[k+1] is greater than zero and equal to or less than the threshold thre_sample, and the distance d_gain[k+1] is equal to or less than the threshold thre _gain, the distance from the gain sample position to the intersection X[k, k+1] is equal to or less than a threshold.

0218For example, when the k-th gain sample position is the head position of the frame, that is, a sample of n = 0, the distance d_sample[k], the distance d_gain[k], the distance d_sample[k+1] and the distance d_gain[k+1] in equation (19) are respectively obtained using the following equation (20) to equation (23). [Math. 20] <maths id="math0020" num="(20)"><math display="block"><mi mathvariant="normal">d</mi><mo>_</mo><mi>sample</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mfenced><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>×</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>/</mo><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced></mfenced></math><img file="EP3608909B1_D0020.tif" /></maths> [Math. 21] <maths id="math0021" num="(21)"><math display="block"><mi mathvariant="normal">d</mi><mo>_</mo><mi>gain</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mi>abs</mi><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>×</mo><mfenced><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>×</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>/</mo><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced></mfenced></mfenced></math><img file="EP3608909B1_D0021.tif" /></maths> [Math. 22] <maths id="math0022" num="(22)"><math display="block"><mi mathvariant="normal">d</mi><mo>_</mo><mi>sample</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>=</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>×</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>/</mo><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced></mfenced></math><img file="EP3608909B1_D0022.tif" /></maths> [Math. 23] <maths id="math0023" num="(23)"><math display="block"><mi mathvariant="normal">d</mi><mo>_</mo><mi>gain</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>=</mo><mi>abs</mi><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>×</mo><mfenced><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>×</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>/</mo><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced></mfenced><mo>+</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced></mfenced></math><img file="EP3608909B1_D0023.tif" /></maths>

0219When it is determined that the conditional expression indicated with equation (19) does not hold true, a gain waveform is obtained through non-linear interpolation, that is, the above-described calculation of equation (4).

0220On the other hand, when it is determined that the conditional expression indicated with equation (19) holds true, a gain waveform is obtained through linear interpolation.

0221For example, when the k-th gain sample position is the head position of the frame, that is, a sample position of n = 0, when the sample position of the intersection X[k, k+1], that is, a sample length from the k-th gain sample position to the intersection X[k, k+1] is set as T'[k], the sample position T'[k] is obtained from the following equation (24). [Math. 24] <maths id="math0024" num="(24)"><math display="block"><mi mathvariant="normal">T</mi><mo>′</mo><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mfenced><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>−</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>×</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced><mo>/</mo><mfenced><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced></mfenced></math><img file="EP3608909B1_D0024.tif" /></maths>

0222Further, a gain value g_interpolated[n] of the sample n which is located between the k-th gain sample position and the intersection X[k, k+1] and which is the n-th (where 0 ≤ n &lt; T'[k]) sample from the head of the frame is calculated from the following equation (25). [Math. 25] <maths id="math0025" num="(25)"><math display="block"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">g</mi><mo>_</mo><mi>interpolated</mi><mfenced open="[" close="]"><mi mathvariant="normal">n</mi></mfenced><mo>=</mo><mi mathvariant="normal">a</mi><mn>1</mn><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>×</mo><mi mathvariant="normal">n</mi><mo>+</mo><mi mathvariant="normal">b</mi><mn>1</mn><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mtd></mtr><mtr><mtd><mfenced><mn>0</mn><mo>≤</mo><mi mathvariant="normal">n</mi><mo>&lt;</mo><mi mathvariant="normal">T</mi><mo>′</mo><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced></mtd></mtr></mtable></math><img file="EP3608909B1_D0025.tif" /></maths>

0223It should be noted that, in equation (25), a1[k] and b1[k] are values respectively obtained from the following equation (26) and equation (27). [Math. 26] <maths id="math0026" num="(26)"><math display="block"><mi mathvariant="normal">a</mi><mn>1</mn><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></math><img file="EP3608909B1_D0026.tif" /></maths> [Math. 27] <maths id="math0027" num="(27)"><math display="block"><mi mathvariant="normal">b</mi><mn>1</mn><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></math><img file="EP3608909B1_D0027.tif" /></maths>

0224al[k] and b1[k] indicate inclination and intercept of the straight line connecting the k-th gain sample position and the intersection X[k, k+1]. Therefore, in this example, as described with reference to <figref idref="f0015">FIG. 17</figref>, it is determined that the gain value linearly changes between the k-th gain sample position G31 and the intersection CP11, and a gain value of each sample n is obtained through linear interpolation.

0225Further, a gain value g_interpolated[n] of the sample n which is located between the intersection X[k, k+1] and the k+1-thgain sample position and which is the n-th (where T'[k] ≤ n &lt; T[k]) sample from the head of the frame is calculated from the following equation (28). [Math. 28] <maths id="math0028" num="(28)"><math display="block"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">g</mi><mo>_</mo><mi>interpolated</mi><mfenced open="[" close="]"><mi mathvariant="normal">n</mi></mfenced><mo>=</mo><mi mathvariant="normal">a</mi><mn>2</mn><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>×</mo><mi mathvariant="normal">n</mi><mo>+</mo><mi mathvariant="normal">b</mi><mn>2</mn><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mtd></mtr><mtr><mtd><mfenced><mi mathvariant="normal">T</mi><mo>′</mo><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>≤</mo><mi mathvariant="normal">n</mi><mo>&lt;</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></mfenced></mtd></mtr></mtable></math><img file="EP3608909B1_D0028.tif" /></maths>

0226It should be noted that, in equation (28), a2[k] and b2[k] are values respectively obtained from the following equation (29) and equation (30). [Math. 29] <maths id="math0029" num="(29)"><math display="block"><mi mathvariant="normal">a</mi><mn>2</mn><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced></math><img file="EP3608909B1_D0029.tif" /></maths> [Math. 30] <maths id="math0030" num="(30)"><math display="block"><mi mathvariant="normal">b</mi><mn>2</mn><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced><mo>=</mo><mi mathvariant="normal">g</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>−</mo><mi mathvariant="normal">s</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi><mo>+</mo><mn>1</mn></mfenced><mo>×</mo><mi mathvariant="normal">T</mi><mfenced open="[" close="]"><mi mathvariant="normal">k</mi></mfenced></math><img file="EP3608909B1_D0030.tif" /></maths>

0227a2[k] and b2[k] indicate inclination and intercept of the straight line connecting the intersection X[k, k+1] and the k+1-th gain sample position. Therefore, in this example, as described with reference to <figref idref="f0015">FIG. 17</figref>, it is determined that the gain value linearly changes between the interception CP11 and the k+1-th gain sample position G32, and a gain value of each sample n is obtained through linear interpolation.

0228As described above, when linear interpolation utilizing the intersection is performed under specific conditions, in the gain decoding processing described with reference to <figref idref="f0014">FIG. 16</figref>, the operation unit 131 performs calculation of the conditional expression indicated with equation (19) based on the read-out gain information in step S132.

0229When the conditional expression indicated with equation (19) holds true, in step S134, the interpolation processing unit 71 calculates the sample position T'[k] of the intersection X[k, k+1] using equation (24) based on the gain value, the sample length and the gain inclination value at the gain sample position read out as the gain information. Further, the interpolation processing unit 71 performs calculation of equation (25) and equation (28) using the obtained sample position T'[k] and generates a gain waveform through linear interpolation.

0230On the other hand, when the conditional expression indicated with equation (19) does not hold true, in step S135, the interpolation processing unit 71 performs non-linear interpolation to generate a gain waveform.

0231In this manner, by performing linear interpolation utilizing the intersection under specific conditions, it is possible to make a difference between the original gain waveform before encoded and the gain waveform obtained through decoding smaller without increasing a processing amount upon encoding.

0232Further, because both linear interpolation and non-linear interpolation can be performed only with a scheme in which non-linear interpolation is performed, it becomes unnecessary to include the interpolation mode information in the gain code string, so that it is possible to lower a bit rate of the output code string. That is, it is possible to reduce a code amount of the output code string.

<Fourth Embodiment>

<Explanation of Gain Decoding Processing>

0233Further, in the third embodiment and modified example 1 of the third embodiment, a case has been described where the interpolation mode information is not included in the gain code string, and non-linear interpolation is basically performed.

0234However, while the interpolation mode information is included in the gain code string, and the gain waveform is basically obtained using an interpolation scheme indicated in the interpolation mode information, when the interpolation scheme indicated in the interpolation mode information is a scheme using non-linear interpolation, linear interpolation may be performed under specific conditions.

0235In such a case, at the decoding apparatus 51, the decoding processing described with reference to <figref idref="f0007">FIG. 8</figref> is performed. However, in the gain decoding processing corresponding to step S43, the gain decoding processing illustrated in <figref idref="f0016">FIG. 18</figref> is performed. The gain decoding processing by the decoding apparatus 51 in <figref idref="f0013">FIG. 15</figref> will be described below with reference to the flowchart of <figref idref="f0016">FIG. 18</figref>.

0236It should be noted that because the processing in step S161 to step S164 is the same as the processing in step S71 to step S74 in <figref idref="f0008">FIG. 9</figref>, explanation thereof will be omitted.

0237In step S163, when it is determined that the scheme is a scheme using non-linear interpolation, in step S165, the operation unit 131 performs calculation of the conditional expression indicated with equation (14) based on the read-out gain information.

0238Then, while the processing in step S166 to step S168 is performed, because these processing is the same as the processing in step S133 to step S135 in <figref idref="f0014">FIG. 16</figref>, explanation thereof will be omitted. It should be noted that, from step S165 to step S168, the processing described in the third embodiment may be performed, or processing described in modified example 1 of the third embodiment may be performed. Further, when non-linear interpolation is performed, limiting processing may be performed.

0239When a gain waveform is generated through interpolation in step S164, step S167 or step S168, the processing then proceeds to step S169.

0240In step S169, the gain decoding circuit 63 determines whether or not processing is performed for all the gain sample positions.

0241When it is determined in step S169 that not all of the gain sample positions is processed, the processing returns to step S161, and the above-described processing is repeated.

0242On the other hand, when it is determined in step S169 that all of the gain sample positions are processed, the gain decoding circuit 63 supplies the gain waveform corresponding to one frame constituted with gain values at the sample positions obtained through the processing so far to the gain applying circuit 64, and the gain decoding processing ends. When the gain decoding processing ends, the processing then proceeds to step S44 in <figref idref="f0007">FIG. 8</figref>.

0243As described above, the decoding apparatus 51 obtains a gain waveform through linear interpolation or non-linear interpolation according to the interpolation mode information. By obtaining the gain waveform through non-linear interpolation as appropriate in this manner according to the interpolation mode information, it is possible to reproduce a gain waveform with high precision with a less code amount.

0244Moreover, even when the interpolation scheme indicated in the interpolation mode information is a scheme using non-linear interpolation, by performing linear interpolation under specific conditions, it is possible to reproduce the original gain waveform with higher precision with a less processing amount of encoding. Further, it is possible to reduce a code amount of the output code string.

0245The series of processes described above can be executed by hardware but can also be executed by software. When the series of processes is executed by software, a program that constructs such software is installed into a computer. Here, the expression "computer" includes a computer in which dedicated hardware is incorporated and a general-purpose personal computer or the like that is capable of executing various functions when various programs are installed.

0246<figref idref="f0017">FIG. 19</figref> is a block diagram showing a hardware configuration example of a computer that performs the above-described series of processing using a program.

0247In such computer, a CPU (Central Processing Unit) 501, a ROM (Read Only Memory) 502, and a RAM (Random Access Memory) 503 are connected to one another by a bus 504.

0248An input/output interface 505 is also connected to the bus 504. An input unit 506, an output unit 507, a recording unit 508, a communication unit 509, and a drive 510 are connected to the input/output interface 505.

0249The input unit 506 is configured from a keyboard, a mouse, a microphone, an imaging device or the like. The output unit 507 is configured from a display, a speaker or the like. The recording unit 508 is configured from a hard disk, a non-volatile memory or the like. The communication unit 509 is configured from a network interface or the like. The drive 510 drives a removable medium 511 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory or the like.

0250In the computer configured as described above, as one example the CPU 501 loads a program recorded in the recording unit 508 via the input/output interface 505 and the bus 504 into the RAM 503 and executes the program to carry out the series of processes described earlier.

0251Programs to be executed by the computer (the CPU 501) are provided being recorded in the removable medium 511 which is a packaged medium or the like. Also, programs may be provided via a wired or wireless transmission medium, such as a local area network, the Internet or digital satellite broadcasting.

0252In the computer, by loading the removable recording medium 511 into the drive 510, the program can be installed into the recording unit 508 via the input/output interface 505. It is also possible to receive the program from a wired or wireless transfer medium using the communication unit 509 and install the program into the recording unit 508. As another alternative, the program can be installed in advance into the ROM 502 or the recording unit 508.

0253It should be noted that the program executed by a computer may be a program that is processed in time series according to the sequence described in this specification or a program that is processed in parallel or at necessary timing such as upon calling.

0254An embodiment of the present technology is not limited to the embodiments described above, and various changes and modifications may be made without departing from the scope of the present technology.

0255For example, the present technology can adopt a configuration of cloud computing which processes by allocating and connecting one function by a plurality of apparatuses through a network.

0256Further, each step described by the above mentioned flow charts can be executed by one apparatus or by allocating a plurality of apparatuses.

0257In addition, in the case where a plurality of processes is included in one step, the plurality of processes included in this one step can be executed by one apparatus or by allocating a plurality of apparatuses.

0258The advantageous effects described herein are not limited, but merely examples. Any other advantageous effects may also be attained.

Reference Signs List

0259<dl id="dl0001" compact="compact"><dt>51</dt><dd>decoding apparatus</dd><dt>61</dt><dd>demultiplexing circuit</dd><dt>62</dt><dd>signal decoding circuit</dd><dt>63</dt><dd>gain decoding circuit</dd><dt>64</dt><dd>gain applying circuit</dd><dt>71</dt><dd>interpolation processing unit</dd><dt>101</dt><dd>limiting processing unit</dd><dt>131</dt><dd>operation unit</dd></dl>