Audio encoder and bandwidth extension decoder

0001Embodiments according to the invention relate to the audio signal processing and, in particular, an audio encoder, a method for providing an output signal, a bandwidth extension decoder and a method for providing a bandwidth extended audio signal.

0002The hearing adapted encoding of audio signals for data reduction for an efficient storage and transmission of these signals has gained acceptance in many fields. Encoding algorithms are known, for instance, as MPEG 1/2 LAYER 3 "MP3" or MPEG 4 AAC. The coding algorithm used for this, in particular when achieving lowest bit rates, leads to the reduction of the audio quality which is often mainly caused by an encoder side limitation of the audio signal bandwidth to be transmitted. A low-pass filtered signal is coded using a so-called core coder and the region with higher frequencies is parameterized so that they can approximately be reconstructed from the low-pass filtered signal.

0003It is known from <patcit id="pcit0001" dnum="WO9857436A"><text>WO 98 57436</text></patcit> to subject the audio signal to a band limiting in such a situation on the encoder side and to encode only a lower band of the audio signal by means of a high quality audio encoder. The upper band, however, is only very coarsely characterized, i.e. by a set of parameters which allow the reproduction of the original spectral envelope of the upper band. On the decoder side, the upper band is then synthesized. For this purpose, a harmonic transposition is proposed, wherein the lower band of the decoded audio signal is supplied to a filterbank. Filterbank channels of the lower band are connected to filterbank channels of the upper band, or are "patched", and each patched bandpass signal is subjected to an envelope adjustment. The synthesis filterbank belonging to a special analysis filterbank here receives bandpass signals of the audio signal in the lower band and envelope-adjusted bandpass signals of the lower band which were harmonically patched into the upper band. The output signal of the synthesis filterbank is an audio signal extended with regard to its audio bandwidth which was transmitted from the encoder side to the decoder side with a very low data rate. In particular, filterbank calculations and patching in the filterbank domain may become a high computational effort.

0004Complexity-reduced methods for a bandwidth extension of band-limited audio signals instead use a copying function of low-frequency signal portions (LF) into the high-frequency range (HF), in order to approximate information missing due to the band limitation. Such methods are described in <nplcit id="ncit0001" npl-type="s"><text>M. Dietz, L. Liljeryd, K. Kjörling and 0. Kunz, "Spectral Band Replication, a novel approach in audio coding," in 112th AES Convention, Munich, May 2002</text></nplcit>; <nplcit id="ncit0002" npl-type="s"><text>S. Meltzer, R. Böhm and F. Henn, "SBR enhanced audio codecs for digital broadcasting such as "Digital Radio Mondiale" (DRM)," 112th AES Convention, Munich, May 2002</text></nplcit>;<nplcit id="ncit0003" npl-type="s"><text> T. Ziegler, A. Ehret, P. Ekstrand and M. Lutzky, "Enhancing mp3 with SBR: Features and Capabilities of the new mp3PRO Algorithm," in 112th AES Convention, Munich, May 2002</text></nplcit>; <nplcit id="ncit0004" npl-type="s"><text>International Standard ISO/IEC 14496-3:2001/FPDAM 1, "Bandwidth Extension</text></nplcit>,"<nplcit id="ncit0005" npl-type="s"><text> ISO/IEC, 2002</text></nplcit>, or "Speech bandwidth extension method and apparatus",<patcit id="pcit0002" dnum="US5455888A"><text> Vasu Iyengar et al. US Patent Nr. 5,455,888</text></patcit>.

0005In these methods no harmonic transposition is performed, but adjacent bandpass filterbank channels of the lower band are artificially introduced into adjacent filterbank channels of the upper band. This leads to a coarse approximation of the upper band of the audio signal. This coarse approximation of the signal is then in a further step refined by defining additional control parameters deduced from the original signal. As an example, the MPEG-4 Standard uses scale factors for adjusting the spectral envelope, a combination of inverse filtering and addition of a noise floor for adapting the tonality, and insertions of sinusoidal signal portions for supplementation of tonal components.

0006Apart from this, further methods exist such as the so-called "blind bandwidth extension", described in<nplcit id="ncit0006" npl-type="s"><text> E. Larsen, R.M. Aarts, and M. Danessis, "Efficient high-frequency bandwidth extension of music and speech", In AES 112th Convention, Munich, Germany, May 2002</text></nplcit> wherein no information on the original HF range is used. Further, also the method of the so-called "Artificial bandwidth extension", exists which is described in <nplcit id="ncit0007" npl-type="s"><text>K. Käyhkö, A Robust Wideband Enhancement for Narrowband Speech Signal; Research Report, Helsinki University of Technology, Laboratory of Acoustics and Audio signal Processing, 2001</text></nplcit>.

0007In <nplcit id="ncit0008" npl-type="s"><text>J. Makinen et al.: AMR-WB+: a new audio coding standard for 3rd generation mobile audio services Broadcasts, IEEE, ICASSP '05</text></nplcit>, a method for bandwidth extension is described, wherein the copying operation of low-frequency components into the high-band is performed by a mirroring operation obtained, for example, by upsampling the low-pass filtered signal.

0008As an alternative, a single side band modulation can be employed which is basically equivalent to a copying operation in the filterbank domain. Methods which enable a harmonic bandwidth extension usually employ a determination step of the pitch (pitch tracking), a non-linear distortion step (see, for example "<nplcit id="ncit0009" npl-type="s"><text>U. Kornagel, Spectral widening of the excitation signal for telephone-band speech enhancement, in: Proceedings of the IWAENC, Darmstadt, Germany, September 2001, pp. 215 -218</text></nplcit>") or make use of phase vocoders as, for example, shown by the US provisional patent application "<patcit id="pcit0003" dnum="US61025129A" dnum-type="L"><text>F.Nagel, S. Disch: "Apparatus and method of harmonic bandwidth extension in audio signals"" with the application number US 61/025129</text></patcit>.

0009The <patcit id="pcit0004" dnum="WO0241302A1"><text>WO 02/41302 A1</text></patcit>, for example, shows a method for enhancing the performance of coding systems that use high-frequency reconstruction methods. It shows how to improve the overall performance of such systems by means of an adaptation over time of the crossover frequency between the low band coded by a core coder and the high band coded by a high-frequency reconstruction system. For this method, the core coder must be able to work with different crossover frequencies at the encoder side as well as at the decoder side. Therefore, the complexity of the core coder is increased.

0010Further technologies for bandwidth extension are described, for example, in "<nplcit id="ncit0010" npl-type="s"><text>R. M. Aarts, E. Larsen, and O. Ouweltjes, A unified approach to low- and high-frequency bandwidth extension. In AES 115th Convention, New York, USA, October 2003</text></nplcit>", <nplcit id="ncit0011" npl-type="b"><text>E. Larsen and R. M. Aarts: Audio Bandwidth Extension - Application to psychoacoustics, Signal Processing and Loudspeaker Design. John Wiley &amp; Sons, Ltd, 2004</text></nplcit>", <nplcit id="ncit0012" npl-type="s"><text>E. Larsen, R. M. Aarts, and M. Danessis: Efficient high-frequency bandwidth extension of music and speech. In AES 112th Convention, Munich, Germany, May 2002</text></nplcit>", "<nplcit id="ncit0013" npl-type="s"><text>J. Makhoul: Spectral Analysis of Speech by Linear Prediction. IEEE Transactions on Audio and Electroacoustics, AU-21(3), June 1973</text></nplcit>", "<patcit id="pcit0005" dnum="US08951029B"><text>United States Patent Application 08/951,029, Ohmori et al.</text></patcit>: Audio band width extending system and method" and "<patcit id="pcit0006" dnum="US6895375B"><text>United States Patent 6895375, Malah, D &amp; Cox, R. VS.</text></patcit>: System for bandwidth extension of Narrow-band speech".

0011Harmonic bandwidth extension methods often exhibit a high complexity, while methods of complexity-reduced bandwidth extension show quality losses. In the particular case where a low bit rate is combined with a small bandwidth of the low band, artifacts such as roughness and a timbre perceived as unpleasant may occur. A reason for this is the fact that the approximated HF portion is based on a copying operation which does not maintain the harmonic relations between the tonal signal portions. This applies both, to the harmonic relation between LF and HF, and also to the harmonic relation between succeeding patches within the HF portion itself. For example, within SBR, the juxtaposition of the coded components and the replicated components, occurring at the boundary between the low and the high bands, may cause rough sound impressions. The reason is illustrated in <figref idref="f0019">Fig. 18</figref> where tonal portions copied from the LF range into the HF range are spectrally densely adjacent to tonal portions of the LF range.

0012<figref idref="f0019">Fig. 18a</figref> shows the original spectrogram 1800a of a signal consisting of three tones. Fittingly, <figref idref="f0019">Fig. 18b</figref> shows a diagram 1800b of the bandwidth extended signal corresponding to the original signal of <figref idref="f0019">Fig. 18a</figref>. The abscissa indicates time and the ordinate indicates frequency. In particular, at the last tone, potential problems 1810 can be observed (smeared lines 1810).

0013If harmonic relations are considered by known methods, this is always done on the basis of an F₀-estimation, as inter alia shown in <patcit id="pcit0007" dnum="US2004028244A1"><text>US 2004/028244 A1</text></patcit>. In this cases, the success of these methods depends primarily on the reliability of this estimation.

0014In general, known bandwidth extension methods provide audio signals at a low bit rate, but with poor audio quality or a good audio quality at high bit rates.

0015It is the object of the present invention to provide an improved coding scheme for audio signals.

0016This object is attained by an audio encoder according to claim 1, a bandwidth extension decoder according to claim 3 and claim 7 and a method according to claims 11, 12 and 13.

0017An embodiment of the invention, as set forth in independent claim 1, provides an audio encoder for providing an output signal using an input audio signal. The audio encoder comprises a patch generator, a comparator and an output interface.

0018The patch generator is configured to generate at least one bandwidth extension high-frequency signal. A bandwidth extension high-frequency signal comprises a high-frequency band, wherein the high-frequency band of the bandwidth extension high-frequency signal is based on a low frequency band of the input audio signal. Different bandwidth extension high-frequency signals comprise different frequencies within their high-frequency bands if different bandwidth extension high-frequency signals are generated.

0019The comparator is configured to calculate a plurality of comparison parameters. A comparison parameter is calculated based on a comparison of the input audio signal and a generated bandwidth extension high-frequency signal. Each comparison parameter of the plurality of comparison parameters is calculated based on a different offset frequency between the input audio signal and a generated bandwidth extension high-frequency signal. Further, the comparator is configured to determine a comparison parameter from the plurality of comparison parameters, wherein the determined comparison parameter fulfills a predefined criterion.

0020In other words, for example, the comparator may be configured to determine the comparison parameter among the plurality of comparison parameters which fulfills at best a predefined criterion.

0021The output interface is configured to provide the output signal for transmission or storage. The output signal comprises a parameter indication based on an offset frequency corresponding to the determined comparison parameter.

0022In other words, the output signal may comprise the selected comparison parameter indicating the optimal offset frequency.

0023Another embodiment of the invention, as set forth in independent claim 3, provides a bandwidth extension decoder for providing a bandwidth extended audio signal based on an input audio signal and a parameter signal. The parameter signal comprises an indication of an offset frequency and an indication of a power density parameter. The bandwidth extension decoder comprises a patch generator, a combiner, and an output interface.

0024The patch generator is configured to generate a bandwidth extension high-frequency signal comprising a high-frequency band. The high-frequency band of the bandwidth extension high-frequency signal is generated based on a frequency shift of a frequency band of the input audio signal. The frequency shift is based on the offset frequency.

0025Further the patch generator is configured to amplify or attenuate the high-frequency band of the bandwidth extension high-frequency signal by a factor equal to the value of the power density parameter or equal to the reciprocal value of the power density parameter, respectively.

0026The combiner is configured to combine the bandwidth extension high-frequency signal and the input audio signal to obtain the bandwidth extended audio signal.

0027The combiner is further configured to ignore a part of the high-frequency band of the bandwidth extension high-frequency signal, wherein the ignored part of the high-frequency band of the bandwidth extension high-frequency signal comprises frequencies lower than an upper cutoff frequency of the input audio signal.

0028The output interface is configured to provide the bandwidth extended audio signal.

0029A further embodiment of the invention, as set forth in independent claim 7, provides a bandwidth extension decoder for providing a bandwidth extended audio signal based on an input audio signal. The bandwidth extension decoder comprises a patch generator, a comparator, a combiner, and an output interface.

0030The patch generator is configured to generate at least one bandwidth extension high-frequency signal comprising a high-frequency band based on the input audio signal, wherein a lower cutoff frequency of the high-frequency band of a generated bandwidth extension high-frequency signal is lower than an upper cutoff frequency of the input audio signal. Different generated bandwidth extension high-frequency signals comprise different frequencies within their high-frequency bands, if different bandwidth extension high-frequency signals are generated.

0031The comparator is configured to calculate a plurality of comparison parameters. A comparison parameter is calculated based on a comparison of the input audio signal and a generated bandwidth extension high-frequency signal. Each comparison parameter of the plurality of comparison parameters is calculated based on a different offset frequency between the input audio signal and the generated bandwidth extension high-frequency signal. Further, the comparator is configured to determine a comparison parameter from the plurality of comparison parameters, wherein the determined comparison parameter fulfills a predefined criterion.

0032In other words, for example, the comparator is configured to determine the comparison parameter among the plurality of comparison parameters which fulfills at best a predefined criterion.

0033The combiner is configured to combine the input audio signal and a bandwidth extension high-frequency signal to obtain the bandwidth extended audio signal, wherein the bandwidth extension high-frequency signal used to obtain the bandwidth extended audio signal is based on an offset frequency corresponding to the determined comparison parameter.

0034The output interface is configured to provide the bandwidth extended audio signal.

0035Embodiments according to the present invention are based on the central idea that a bandwidth extension high-frequency signal which is also called patch, may be generated and compared with the original input audio signal. By using a different offset frequency of the bandwidth extension high-frequency signal or several bandwidth extension high-frequency signals with different offset frequencies, a plurality of comparison parameters corresponding to the different offset frequencies may be calculated. The comparison parameters may be related to a quantity associated with the audio quality. Therefore, a comparison parameter may be determined assuring the compatibility of the bandwidth extension high-frequency signal and the input audio signal, and as a consequence making the audio quality improve.

0036The bit rate for transmission or storage of the encoded audio signal may be decreased by using a parameter indication based on the offset frequency corresponding to the determined comparison parameter for a reconstruction of the high-frequency band of the original input audio signal. In this way, only a low frequency portion of the input audio signal and the parameter indication need to be stored or transmitted.

0037The terms comparison parameter, xover frequency and parameter indication will be defined later on.

0038Some preferred embodiments according to the invention relate to a comparator using a cross correlation for the comparison of the input audio signal and the generated bandwidth extension high-frequency signal to calculate the comparison parameter.

0039Some further preferred embodiments according to the invention relate to a patch generator, generating the bandwidth extension high-frequency signal in the time domain based on a single side band modulation.

0040It is an advantage of preferred embodiments of the invention that an improved coding scheme for audio signals which allow increasing the audio quality and/or decreasing the bit rate for transmission or storage, is provided.

0041Embodiments according to the invention will be detailed subsequently referring to the appended drawings, in which: <dl id="dl0001"><dt>Fig. 1</dt><dd>is a block diagram of an audio encoder;</dd><dt>Fig. 2</dt><dd>is a schematic illustration of a bandwidth extension high-frequency signal generation, a comparison of the input audio signal and a generated bandwidth extension high-frequency signal and a power adaptation of the bandwidth extension high-frequency signal;</dd><dt>Fig. 3</dt><dd>is a schematic illustration of a bandwidth extension high-frequency signal generation, a comparison of the input audio signal and a bandwidth extension high-frequency signal and a power adaptation of the bandwidth extension high-frequency signal;</dd><dt>Fig. 4</dt><dd>is a block diagram of an bandwidth extension encoder;</dd><dt>Fig. 5</dt><dd>is a block diagram of a bandwidth extension decoder;</dd><dt>Fig. 6</dt><dd>is a block diagram of a bandwidth extension decoder;</dd><dt>Fig. 7</dt><dd>is a flow chart of a method for providing an output signal based on an input audio signal;</dd><dt>Fig. 8</dt><dd>is a flow chart of a method for providing a bandwidth extended audio signal;</dd><dt>Fig. 9</dt><dd>is a flow chart of a method for providing an output signal based on an input audio signal;</dd><dt>Fig. 10</dt><dd>is a flow chart of a method for calculating a comparison parameter;</dd><dt>Fig. 11</dt><dd>is a schematic illustration of an interpolation of the offset frequency;</dd><dt>Fig. 12</dt><dd>is a block diagram of a bandwidth extension decoder;</dd><dt>Fig. 13</dt><dd>is a flow chart of a method for providing a bandwidth extended audio signal;</dd><dt>Fig. 14</dt><dd>is a block diagram of a method for providing a bandwidth extended audio signal;</dd><dt>Fig. 15</dt><dd>is a block diagram of an bandwidth extension encoder;</dd><dt>Fig. 16a</dt><dd>is a spectrogram of three tones using variable crossover frequency;</dd><dt>Fig. 16b</dt><dd>is a spectrogram of the original audio signal of three tones;</dd><dt>Fig. 17</dt><dd>is a power spectrum diagram of an original audio signal, a bandwidth extended audio signal using constant crossover frequency and a bandwidth extended audio signal using variable crossover frequency;</dd><dt>Fig. 18a</dt><dd>is a spectrogram of three tones using a known bandwidth extension method; and</dd><dt>Fig. 18b</dt><dd>is a spectrogram of the original audio signal of three tones.</dd></dl>

0042In the following, the same reference numerals are partly used for objects and functional units having the same or similar functional properties and the description thereof with regard to a figure shall apply also to other figures in order to reduce redundancy in the description of the embodiments.

0043<figref idref="f0001">Fig. 1</figref> shows a block diagram of an audio encoder 100 for providing an output signal 132 according to an embodiment of the invention, using an input audio signal 102. The output signal is suitable for a bandwidth extension at a decoder. Therefore the audio encoder is also called bandwidth extension encoder. The bandwidth extension encoder 100 comprises a patch generator 110, a comparator 120 and an output interface 130. The patch generator 110 is connected to the comparator 120 and the comparator 120 is connected to the output interface 130.

0044The patch generator 110 generates at least one bandwidth extension high-frequency signal 112. A bandwidth extension high-frequency signal 112 comprises a high-frequency band, wherein the high-frequency band of the bandwidth extension high-frequency signal 112 is based on a low frequency band of the input audio signal 102. If different bandwidth extension high-frequency signals 112 are generated, the different bandwidth extension high-frequency signals 112 comprise different frequencies within their high-frequency bands.

0045The comparator 120 calculates a plurality of comparison parameters. A comparison parameter is calculated based on a comparison of the input audio signal 102 and a generated bandwidth extension high-frequency signal 112. Each comparison parameter of the plurality of comparison parameters is calculated based on a different offset frequency between the input audio signal 102 and a generated bandwidth extension high-frequency signal 112. Further, the comparator 120 determines a comparison parameter from the plurality of comparison parameters, wherein the determined comparison parameter fulfills a predefined criterion.

0046The output interface 130 provides the output signal 132 for transmission or storage. The output signal 132 comprises a parameter indication based on an offset frequency corresponding to the determined comparison parameter.

0047By calculating a plurality of comparison parameters for different offset frequencies, a bandwidth extension high-frequency signal 112 may be found which fits well to the original input audio signal 102. This may be done by generating a plurality of bandwidth extension high-frequency signals 112 each with a different offset frequency or by generating one bandwidth extension high-frequency signal and shifting the high frequency band of the bandwidth extension high-frequency signal 112 by different offset frequencies. Also a combination of generating a plurality of bandwidth extension high-frequency signals 112 with different offset frequencies and shifting the high frequency band of them by other different offset frequencies may be possible. For example, five different bandwidth extension high-frequency signals 112 are generated and each of them is shifted five times by a constant frequency offset.

0048<figref idref="f0002">Fig. 2</figref> shows a schematic illustration 200 of a bandwidth extension high-frequency signal generation, a comparison of the bandwidth extension high-frequency signal and the input audio signal and an optional power adaptation of the bandwidth extension high-frequency signal for the case that only one bandwidth extension high-frequency signal is generated and shifted by different offset frequencies.

0049The first schematic "power vs. frequency" diagram 210 shows schematically an input audio signal 102. Based on this input audio signal 102, the patch generator 110 may generate the bandwidth extension high-frequency signal 112, for example, by shifting 222 a low frequency band of the input audio signal 102 to higher frequencies (as indicated by reference numeral). For example, the low frequency band is shifted by a frequency equal to a crossover frequency of a core coder, not illustrated in <figref idref="f0001">Fig. 1</figref>, which may be a part of the bandwidth extension encoder 100 or another predefined frequency.

0050The generated bandwidth extension high-frequency signal 112 may then be shifted by different offset frequencies 232 and for each offset frequency 232 (as indicated by reference numeral 230), a comparison parameter may be calculated by the comparator 120. The offset frequency 232 may be, for example, defined relative to a crossover frequency of a core coder, relative to another specific frequency or may be defined as an absolute frequency value.

0051Next, the comparator 120 determines a comparison parameter fulfilling the predefined criterion. In this way, a bandwidth extension high-frequency signal 112 with an offset frequency 242 corresponding to the determined comparison parameter may be determined (as shown at reference numeral 240).

0052Additionally, also a power density parameter 252 may be determined (as indicated by reference numeral 250). The power density parameter 252 may indicate a ratio of the high-frequency band of the bandwidth extension high-frequency signal with the offset frequency corresponding to the determined comparison parameter and a corresponding frequency band of the input audio signal. For example, the ratio may relate to a power density ratio, a power ratio, or another ratio of a quantity related to the power density of a frequency band.

0053Alternatively, <figref idref="f0003">Fig. 3</figref> shows a schematic illustration 300 of a bandwidth extension high-frequency signal generation, a comparison of the generated bandwidth extension high-frequency signals and the input audio signal and an optional power adaptation of the bandwidth extension high-frequency signal for the case that a plurality of bandwidth extension high-frequency signals with different offset frequencies are generated.

0054In difference to the sequence shown in <figref idref="f0002">Fig. 2</figref>, the patch generator 110 generates a plurality of bandwidth extension high-frequency signals 112 with different offset frequencies 232 (as indicated by reference numeral 320). This may again be done by a frequency shift 222 of a low frequency band of the input audio signal 102 to higher frequencies. The low frequency band of the input audio signal 102 may be shifted by a constant frequency plus the individual offset frequency 232 of each bandwidth extension high-frequency signal 112. The constant frequency may be equal to the crossover frequency of the core coder or another specific frequency.

0055A comparison parameter for each generated bandwidth extension high-frequency signal 112 may then be calculated and the comparison parameter fulfilling the predefined criterion may be determined 240 by the comparator 120.

0056The power density parameter may be determined 250 as described before.

0057The concepts shown in <figref idref="f0002">Figs. 2</figref> and <figref idref="f0003">3</figref> may also be combined.

0058The comparison of the input audio signal 102 and the generated bandwidth extension high-frequency signal 112 may be done by a cross correlation of both signals. In this case, a comparison parameter may be, for example, the result of a cross correlation for a specific offset frequency between the input audio signal 102 and a generated bandwidth extension high-frequency signal 112.

0059The parameter indication of the output signal 132 may be the offset frequency itself, a quantized offset frequency or another quantity based on the offset frequency.

0060By transmitting or storing only the parameter indication instead of the high-frequency band of the input audio signal 102, the bit rate for transmission or storage may be reduced. By choosing the parameter based on the offset frequency corresponding to a comparison parameter fulfilling a predefined criterion, this may yield in a better audio quality than decoding only the band-limited audio signal.

0061A predefined criterion may be to determine a comparison parameter of the plurality of comparison parameters indicating, for example, a bandwidth extension high-frequency signal 112 with an corresponding offset frequency matching the input audio signal 102 better than 70% of the bandwidth extension high-frequency signals 112 with other offset frequencies, indicating a bandwidth extension high-frequency signal 112 with an corresponding offset frequency being one of the best three matches to the input audio signal 102 or indicating a best-matching bandwidth extension high-frequency signal 112 with an corresponding offset frequency. This relates to the case where a plurality of bandwidth extension high-frequency signals 112 with different offset frequencies are generated as well as to the case where only one bandwidth extension high-frequency signal 112 is generated and shifted by different offset frequencies or a combination of these two cases.

0062A comparison parameter may be the result of a cross correlation or another quantity indicating how well a bandwidth extension high-frequency signal 112 with a specific offset frequency matches the input audio signal 102.

0063The bandwidth extension encoder 100 may comprise a core coder for encoding a low frequency band of the input audio signal 102. This core coder may comprise a crossover frequency which may correspond to the upper cutoff frequency of the encoded low frequency band of the input audio signal 102. The crossover frequency of the core coder may be constant or variable over time. Implementing a variable crossover frequency may increase the complexity of the core coder, but may also increase the flexibility for encoding.

0064The process shown in <figref idref="f0002">Fig. 2</figref> and/or <figref idref="f0003">Fig. 3</figref> may be repeated for higher frequency bands or patches. For example, the low frequency band of the input audio signal 102 comprises an upper cutoff frequency of 4 kHz. Therefore, if the low frequency band of the input audio signal 102 is shifted by the upper cutoff frequency of the low frequency band to generate the bandwidth extension high-frequency signal 112, the bandwidth extension high-frequency signal 112 comprises a high-frequency band with a lower cutoff frequency of 4 KHz and an upper cutoff frequency of 8 kHz. The process may be repeated by shifting a low frequency band of the input audio signal 102 by two times the upper cutoff frequency of the low frequency band. So, the new generated bandwidth extension high-frequency signal 112 comprises a high-frequency band with a lower cutoff frequency of 8 KHz and an upper cutoff frequency of 12 kHz. This may be repeated until a desired highest frequency is reached.

0065Alternatively, this may also be realized by generating one bandwidth extension high frequency signal with a plurality of different high frequency bands.

0066As illustrated in this example, the bandwidth of the low frequency band of the input audio signal and the bandwidth of a high frequency band of a bandwidth extension high frequency signal may be the same. Alternatively, the low frequency band of the input audio signal may be spread and shifted to generate the bandwidth extension high frequency signal.

0067Determining a bandwidth extension high-frequency signal 112 with an offset frequency 232 corresponding to the determined comparison parameter may leave a gap between the low frequency band of the input audio signal 102 and the high frequency band of the bandwidth extension high-frequency signal 112 depending on the offset frequency 242. This gap may be filled by generating frequency portions fitting this gap containing e.g. band limited noise. Alternatively, the gap may be left empty, since the audio quality may not suffer dramatically.

0068<figref idref="f0004">Fig. 4</figref> shows a block diagram of an bandwidth extension encoder 400 for providing an output signal 132 using an input audio signal 102 according to a preferred embodiment of the invention. The bandwidth extension encoder 400 comprises a patch generator 110, a comparator 120, an output interface 130, a core coder 410, a bandpass filter 420 and a parameter extraction unit 430. The core coder 410 is connected to the output interface 130 and the patch generator 110, the patch generator 110 is connected to the comparator 120, the comparator 120 is connected to the parameter extraction unit 430, the parameter extraction unit 430 is connected to the output interface 130 and the bandpass filter 420 is connected to the comparator 120.

0069The patch generator 110 may be realized as a modulator for generating the bandwidth extension high-frequency signal 112 based on the input audio signal 102. The comparator 120 may perform the comparison of the input audio signal 102 filtered by the bandpass filter 420 and the generated bandwidth extension high-frequency signal 112 by a cross correlation of them. The determination of the comparison parameter fulfilling the predefined criterion may also be called lag estimation.

0070The output interface 130 may also include a functionality of a bitstream formatter and may comprise a combiner for combining a low frequency signal provided by the core coder 410 and a parameter signal 432 comprising the parameter indication based on the offset frequency provided by the parameter extraction unit 430. Further, the output interface 130 may comprise an entropy coder or a differential coder to reduce the bit rate of the output signal 132. The combiner and the entropy or differential coder may be part of the output interface 130 as shown in this example or may be independent units.

0071The audio signal 102 may be divided in a low frequency part and a high-frequency part. This may be done by a low-pass filter of the core coder 410 and the band-pass filter 420. The low-pass filter may be part of the core coder 410 or an independent low-pass filter connected to the core coder 410.

0072The low frequency part is processed by a core encoder 410 which can be an audio coder, for example, conforming to the MPEG1/2 Layer 3 "MP3" or MPEG 4 AAC standard or a speech coder.

0073The low frequency part may be shifted by a fixed value, for example, by means of a side band modulation or a Fast Fourier transformation (FFT) in the frequency domain, so that it is located above the original low frequency region in the target area of the corresponding patch. Optional, the low frequency part may be obtained directly from the input signal 102. This may be done by an independent low-pass filter connected to the patch generator 110.

0074In regular time intervals, the cross correlation between amplitude spectra of windowed signal sections between the original high-frequency part (of the input audio signal) and the obtained high-frequency part (the bandwidth extension high-frequency signal) may be calculated. In this way, the lag (the offset frequency) for maximum correlation may be determined. This lag may have the meaning of a correction factor in terms of the original single side band modulation, i.e. the single side band modulation may be additionally corrected by the lag to maximize the cross correlation. In other words, the offset frequency, which is also called lag, corresponding to the comparison parameter fulfilling the predefined criterion may be determined, wherein the comparison parameter corresponds to the cross correlation and the predefined criterion may be finding the maximum correlation.

0075In addition, the ratios of the absolute values of the amplitude spectra may be determined. By this, it may be derived by which factor the obtained high-frequency signal should be attenuated or amplified. In other words, a power density parameter may be determined indicating a ratio of the power, the power densities, the absolute values of the amplitude spectra or another value related to the power density ratio between the high-frequency band of the bandwidth extension high-frequency signal 112 and a corresponding frequency band of the original input audio signal 102. This may be done by a power density comparator which may be a part of the parameter extraction unit 430 as in the shown example or an independent unit. For determining the power density parameter, for example, the bandwidth extension high-frequency signal 112 which was generated by shifting the low frequency band of the input audio signal 102 by a constant frequency or the bandwidth extension high-frequency signal 112 corresponding to the determined comparison parameter or another generated bandwidth extension high-frequency signal 112 may be used. A corresponding frequency band in this case means, for example, a frequency band with the same frequency range. For example, if the high frequency band of the bandwidth extension high frequency signal comprises frequencies form 4 kHz to 8 kHz, then the corresponding frequency band of the input audio signal comprises also the range from 4 kHz to 8 kHz.

0076The obtained correction factors (offset frequency, power density parameter) corresponding to the lag and corresponding to the absolute value of the amplitude may be interpolated over time. In other words, a parameter determined for a windowed signal section (for a time frame) may be interpolated for each time step of the signal section.

0077This modulation (control) signal (parameter signal) or a parameterized representation of it may be stored or transmitted to a decoder. In other words, the parameter signal 432 may be combined with the low frequency band of the input audio signal 102 processed by the core coder 410 to obtain the output signal 132 which may be stored or transmitted to a decoder.

0078Additionally, further parameters for adapting, for example, a noise level and/or the tonality may be determined. This may be done by the parameter extraction unit 430. The further parameters may be added to the parameter signal 432.

0079The example shown in <figref idref="f0004">Fig. 4</figref> illustrates an encoder-sided calculation of a time variable modulation. Time variable modulation in this case relates to the bandwidth extension high-frequency signals 112 with different offset frequencies. The offset frequency corresponding to the determined comparison parameter fulfilling the predefined criterion may vary over time.

0080<figref idref="f0005">Fig. 5</figref> shows a block diagram of a bandwidth extension decoder 500 for proving a bandwidth extended audio signal 532 based on an input audio signal 502 and a parameter signal 504 according to an embodiment of the invention. The parameter signal 504 comprises an indication of an offset frequency and an indication of a power density parameter. The bandwidth extension decoder 500 comprises a patch generator 510, a combiner 520 and an output interface 530. The patch generator 510 is connected to the combiner 520 and the combiner 520 is connected to the output interface 530.

0081The patch generator 510 generates a bandwidth extension high-frequency signal 512 comprising a high-frequency band based on the input audio signal 502. The high-frequency band of the bandwidth extension high-frequency signal 512 is generated based on a frequency shift of a frequency band of the input audio signal 502, wherein the frequency shift is based on the offset frequency.

0082Further, the patch generator 510 amplifies or attenuates the high-frequency band of the bandwidth extension high-frequency signal 512 by a factor equal to the value of the power density parameter or equal to the reciprocal value of the power density parameter.

0083The combiner 520 combines the bandwidth extension high-frequency signal 512 and the input audio signal 502 to obtain the bandwidth extended audio signal 532 and the output interface 530 provides the bandwidth extended audio signal 532.

0084Generating the bandwidth extension high-frequency signal 112 based on the offset frequency may allow an improved continuation of the frequency range of the input audio signal in the high-frequency region, for example, if the offset frequency is determined as described before. This may increase the audio quality of the bandwidth extended audio signal 532.

0085Additionally, the power density of the high-frequency continuation of the input audio signal 502 may be done in a very efficient way by amplifying or attenuating the high-frequency band of the bandwidth extension high-frequency signal 512 by the power density parameter. In this way, a normalization may not be necessary.

0086The patch generator 510 may generate the bandwidth extension high-frequency signal 512 by shifting the frequency band of the input audio signal 512 by a constant frequency plus the offset frequency. The combiner is configured to ignore a part of the high-frequency band of the bandwidth extension high-frequency signal 512 comprising frequencies lower than an upper cutoff frequency of the input audio signal 502.

0087The patch generator 510 may generate the bandwidth extension high-frequency signal 512 in the time domain or in the frequency domain. In the time domain, the patch generator 510 may generate the bandwidth extension high-frequency signal 512 based on a single side band modulation.

0088Additionally, the output interface may amplify the output signal before providing it.

0089<figref idref="f0006">Fig. 6</figref> shows a block diagram of a bandwidth extension decoder 600 for providing a bandwidth extended audio signal 532 based on an input audio signal 502 and a parameter signal 504 according to a preferred embodiment of the invention. The bandwidth extension decoder 600 comprises a patch generator

0090510, a combiner 520, an output interface 530, a core decoder 610 and a parameter extraction unit 620. The core decoder 610 is connected to the patch generator 510 and the combiner 520, the parameter extraction unit 620 is connected to the patch generator 510 and to the output interface 530, the patch generator 510 is connected to the combiner 520 and the combiner 520 is connected to the output interface 530.

0091The core decoder 610 may decode the received bit stream 602 and provide the input audio signal 502 to the patch generator 510 and the combiner 520. The input audio signal 502 may comprise an upper cutoff frequency equal to a crossover frequency of the core decoder 610. This crossover frequency may be constant or variable over time. Variable over time means, for example, variable for different time intervals or time frames, but constant for one time interval or time frame.

0092The parameter extraction unit 620 may separate the parameter signal 504 from the received bit stream 602 and provide it to the patch generator 510. Additionally, the parameter signal 504 or an extracted noise and/or tonality parameter may be provided to the output interface 530.

0093The patch generator 510 may modulate the input audio signal 502 based on the offset frequency to obtain the bandwidth extension high-frequency signal 512 and may amplify or attenuate the bandwidth extension high-frequency signal 512 based on the power density parameter comprised in the parameter signal 504. This bandwidth extension high-frequency signal 512 is provided to the combiner 530. In other words, the patch generator 510 may modulate the input audio signal 502 based on the offset frequency and the power density parameter to obtain a high-frequency signal. This may be done, for example, in the time domain by a single side band modulation 634 with an interpolation and/or filtering 632 for each time step.

0094The combiner 520 combines the input audio signal 502 and the generated bandwidth extension high-frequency signal 512 to obtain the bandwidth extension audio signal 532.

0095The output interface 530 provides the bandwidth extended audio signal 532 and may additionally comprise a correction unit. The correction unit may carry out a tonality correction and/or a noise correction based on parameters provided by the parameter extraction unit 620. The correction unit may be part of the output interface 530 as shown in <figref idref="f0006">Fig. 6</figref> or may be an independent unit. The correction unit may also be arranged between the patch generator 510 and the combiner 520. In this way, the correction unit may only correct tonality and/or noise of the generated bandwidth extension high-frequency signal 512. A tonality and noise correction of the input audio signal 512 is not necessary since the input audio signal 502 corresponds to the original audio signal.

0096Summarized in some words, the bandwidth extension decoder 600 may synthesize and spectrally form a high-frequency signal out of an output signal of the audio decoder or core decoder (the input audio signal) by means of the transmitted modulation function. Transmitted modulation function, for example, means a modulation function based on the offset frequency and on the power density parameter. Then the high-frequency signal and the low frequency signal may be combined and further parameters for adapting the noise level and tonality may be applied.

0097<figref idref="f0007">Fig. 7</figref> shows a flowchart of a method 700 for providing an output signal based on an input audio signal according to an embodiment of the invention. The method comprises generating 710 at least one bandwidth extension high-frequency signal, calculating 720 a plurality of comparison parameters, determining 730 a comparison parameter from the plurality of comparison parameters and providing 740 the output signal for transmission or storage.

0098A generated bandwidth extension high-frequency signal comprises a high-frequency band. The high-frequency band of the bandwidth extension high-frequency signal is based on a low frequency band of the input audio signal. Different bandwidth extension high-frequency signals comprise different frequencies within their high-frequency bands, if different bandwidth extension high-frequency signals are generated.

0099A comparison parameter is calculated based on a comparison of the input audio signal and a generated bandwidth extension high-frequency signal. Each comparison parameter of the plurality of comparison parameters is calculated based on a different offset frequency between the input audio signal and a generated bandwidth extension high-frequency signal.

0100The determined comparison parameter fulfills a predefined criterion.

0101The output signal comprises a parameter indication based on an offset frequency corresponding to the determined comparison parameter.

0102<figref idref="f0008">Fig. 8</figref> shows a flowchart of a method 800 for providing a bandwidth extended audio signal based on an input audio signal and a parameter signal according to an embodiment of the invention. The parameter signal comprises an indication of an offset frequency and an indication of a power density parameter. The method comprises generating 810 a bandwidth extension high-frequency signal, amplifying 820 or attenuating the high-frequency band of the bandwidth extension high-frequency signal, combining 830 the bandwidth extension high-frequency signal and the input audio signal to obtain the bandwidth extended audio signal and providing 840 the bandwidth extended audio signal.

0103The bandwidth extension high-frequency signal comprises a high-frequency band. The high-frequency band of the bandwidth extension high-frequency signal is generated 810 based on a frequency shift of a frequency band of the input audio signal. The frequency shift is based on the offset frequency.

0104The high-frequency band of the bandwidth extension high-frequency signal is amplified 820 or attenuated by a factor equal to the value of the power density parameter or equal to the reciprocal value of the power density parameter.

0105<figref idref="f0009">Fig. 9</figref> shows a flowchart of a method 900 for providing and output signal based on an input audio signal. It illustrates one possibility for the sequence of the algorithm in the encoder. This may also be formal mathematically described in the following. Real time signals may be indicated by Latin lower case letters, Hilbert transformed signals with corresponding Greek and Fourier transformed signals with Latin capital letters or alternatively Greek ones.

0106The input signal may be called f(n), the output signal o (n). <i>f_{HF<sub2>k</sub2>}</i> = <i>f * filt_{BF<sub2>k</sub2>}; 1 < k < k_max</i> indicates the Fourier transformed, j indicated the imaginary number and the Hilbert transformation H(.) is defined as usual: <maths id="math0001"><math display="block"><mrow><mi>ϕ</mi><mfenced><mi>m</mi></mfenced><mo>:</mo><mo>=</mo><mi mathvariant="script">H</mi><mfenced><mi>f</mi><mfenced><mi>n</mi></mfenced></mfenced><mo>=</mo><msup><mi mathvariant="script">F</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mfenced><mi>j</mi><mo>⋅</mo><mi>sgn</mi><mfenced><mi mathvariant="italic">ω</mi></mfenced><mo>⋅</mo><mi>F</mi><mfenced><mi mathvariant="italic">jω</mi></mfenced></mfenced></mrow></math><img file="EP2359366B1_D0001.tif" /></maths> with <maths id="math0002"><math display="block"><mrow><mi>F</mi><mfenced><mi mathvariant="italic">jω</mi></mfenced><mo>:</mo><mo>=</mo><mi mathvariant="script">F</mi><mfenced><mi>f</mi><mfenced><mi>n</mi></mfenced></mfenced></mrow></math><img file="EP2359366B1_D0002.tif" /></maths> xOver may be the cutoff frequency of the core coder, <maths id="math0003"><math display="inline"><mrow><mi mathvariant="normal">n</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi></mrow></math><img file="EP2359366B1_D0003.tif" /></maths> may indicate a time. <maths id="math0004"><math display="inline"><mrow><msub><mi mathvariant="normal">k</mi><mi mathvariant="normal">max</mi></msub><mo>></mo><mi mathvariant="normal">k</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi></mrow></math><img file="EP2359366B1_D0004.tif" /></maths> may indicate the k-th extension or patch. α_k describes a band edge of perceptual bands related to xOver, for example, according to the Bark or the ERB-scale. Alternatively, the α_k may, for example, increase linearly, i.e. α_k+1-α_k ≡ constant. The Hilbert transformation can also be calculated computationally efficient by filtering the signal with a modulated low-pass filter.

0107First, an analytical modulator function 902 with the modulation frequencies α_k and the resulting phase increments <maths id="math0005"><math display="inline"><mrow><msub><mi>γ</mi><mi>k</mi></msub><mo>:</mo><mo>=</mo><mfrac><mrow><msub><mi>α</mi><mi>k</mi></msub></mrow><mi mathvariant="italic">Fs</mi></mfrac></mrow></math><img file="EP2359366B1_D0005.tif" /></maths> with the time increment <maths id="math0006"><math display="inline"><mrow><mfrac><mn>1</mn><mi mathvariant="italic">Fs</mi></mfrac></mrow></math><img file="EP2359366B1_D0006.tif" /></maths> (Fs indicates the sampling rate) may be generated. This may be mathematically described in the following formulas: <maths id="math0007"><math display="block"><mrow><msub><mi>μ</mi><mi>k</mi></msub><mfenced><mi>n</mi></mfenced><mo>:</mo><mo>=</mo><msup><mi>e</mi><mrow><mn>2</mn><mi mathvariant="italic">πj</mi><mrow><mstyle displaystyle="true"><mrow><munderover><mrow><mo>∑</mo></mrow><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover></mrow></mstyle><mrow><msub><mi>γ</mi><mi>k</mi></msub></mrow></mrow></mrow></msup><mo>=</mo><msup><mi>e</mi><mrow><mn>2</mn><mi mathvariant="italic">πj</mi><msub><mi>γ</mi><mi>k</mi></msub><mi>n</mi></mrow></msup></mrow></math><img file="EP2359366B1_D0007.tif" /></maths><maths id="math0008"><math display="block"><mrow><mi>μ</mi><mfenced><mi>n</mi></mfenced><mo>:</mo><mo>=</mo><mrow><mstyle displaystyle="true"><mrow><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>k</mi><mi>max</mi></msub></mrow></munderover></mrow></mstyle><mrow><msup><mi>e</mi><mrow><mn>2</mn><mi mathvariant="italic">πj</mi><mrow><mstyle displaystyle="true"><mrow><munderover><mrow><mo>∑</mo></mrow><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover></mrow></mstyle><mrow><msub><mi>γ</mi><mi>k</mi></msub></mrow></mrow></mrow></msup></mrow></mrow><mo>=</mo><mrow><mstyle displaystyle="true"><mrow><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>k</mi><mi>max</mi></msub></mrow></munderover></mrow></mstyle><mrow><msup><mi>e</mi><mrow><mn>2</mn><mi mathvariant="italic">πj</mi><msub><mi>γ</mi><mi>k</mi></msub><mi>n</mi></mrow></msup></mrow></mrow></mrow></math><img file="EP2359366B1_D0008.tif" /></maths>

0108The sum may only be replaced by n, if γ<i>_k</i> is independent of n.

0109The input audio signal 102 or real audio signal f may be bandpass filtered to a bandwidth of α_k+1-α_k which may be expressed by: <maths id="math0009"><math display="block"><mrow><msub><mi>f</mi><mi mathvariant="italic">LF</mi></msub><mo>=</mo><mi>f</mi><mo>*</mo><msub><mi mathvariant="italic">filt</mi><mi mathvariant="italic">LF</mi></msub></mrow></math><img file="EP2359366B1_D0009.tif" /></maths>

0110In this case, each patch will comprise the same bandwidth.

0111Alternatively, the input audio signal f 102 may be band-pass filtered to bandwidths of α_k with different bandwidths which can be described by: <maths id="math0010"><math display="block"><mrow><msub><mi>f</mi><mrow><msub><mi mathvariant="italic">LF</mi><mi>k</mi></msub></mrow></msub><mo>=</mo><mi>f</mi><mo>*</mo><msub><mi mathvariant="italic">filt</mi><mrow><msub><mi mathvariant="italic">LF</mi><mi>k</mi></msub></mrow></msub></mrow></math><img file="EP2359366B1_D0010.tif" /></maths>

0112Then the areas of the original signal may be determined which should be reconstructed by this method. These band limited regions may be indicated as: <maths id="math0011"><math display="block"><mrow><msub><mi>f</mi><mrow><msub><mi mathvariant="italic">HF</mi><mi>k</mi></msub></mrow></msub><mo>=</mo><mi>f</mi><mo>*</mo><msub><mi mathvariant="italic">filt</mi><mrow><msub><mi mathvariant="italic">BF</mi><mi>k</mi></msub></mrow></msub><mo>;</mo><mspace width="1em" /><mn>1</mn><mo>&lt;</mo><mi>k</mi><mo>&lt;</mo><msub><mi>k</mi><mi>max</mi></msub></mrow></math><img file="EP2359366B1_D0011.tif" /></maths> and are located in the intervals (α_k, α_k+1).

0113The modulation of the low-pass filtered input signals 904 may be done in the frequency domain or in the time domain.

0114In the frequency domain the input signals may be windowed first which may be described by: <maths id="math0012"><math display="block"><mrow><msub><mi>f</mi><mi>ξ</mi></msub><mfenced><mi>n</mi></mfenced><mo>=</mo><mi>f</mi><mfenced><mi>ξ</mi><mo>⋅</mo><mfrac><mi mathvariant="italic">NFFT</mi><mn>2</mn></mfrac><mo>+</mo><mi>mod</mi><mfenced separators=","><mi>n</mi><mi mathvariant="italic">NFFT</mi></mfenced><mo>+</mo><mn>1</mn></mfenced><mo>⋅</mo><mi>win</mi><mfenced><mi>mod</mi><mfenced separators=","><mi>n</mi><mi mathvariant="italic">NFFT</mi></mfenced><mo>+</mo><mn>1</mn></mfenced></mrow></math><img file="EP2359366B1_D0012.tif" /></maths> wherein NFFT is the number of fast Fourier transformation bins (for example 512 bins), ξ is the window number and win(.) is a window function. The windows or time frames may comprise a temporarily overlap. For example, the formula given above describes a temporal overlap of half a window. Thus, <maths id="math0013"><math display="inline"><mrow><mi mathvariant="normal">n</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi></mrow></math><img file="EP2359366B1_D0013.tif" /></maths> blocks out of the original signal and with it connected as many amplitude spectra F_ξ(ω) with ξ ≤ N as absolute values of the Fourier transformed <maths id="math0014"><math display="block"><mrow><msub><mrow><mover><mi>γ</mi><mrow><mo>^</mo></mrow></mover></mrow><mi>k</mi></msub><mo>:</mo><mo>=</mo><mrow><mo>⌊</mo><msub><mi>γ</mi><mi>k</mi></msub><mo>⋅</mo><mi mathvariant="italic">NFFT</mi><mo>⌋</mo></mrow></mrow></math><img file="EP2359366B1_D0014.tif" /></maths> describes the index of the band edge k in the Fourier transformed.

0115Then the signal is modulated in the frequency domain by shifting of the FFT-bins (fast Fourier transformation bins). The implicit Hilbert transformation is here not necessary, but it makes an equal formal description of the following steps possible: <maths id="math0015"><math display="block"><mrow><msub><mi mathvariant="normal">Ψ</mi><mi>ξ</mi></msub><mfenced><mi>ω</mi><mo>+</mo><msub><mrow><mover><mi>γ</mi><mrow><mo>^</mo></mrow></mover></mrow><mi>k</mi></msub></mfenced><mo>:</mo><mo>=</mo><msub><mi>F</mi><mi>ξ</mi></msub><mfenced><mi>ω</mi></mfenced><mo>;</mo><msub><mi mathvariant="normal">Φ</mi><mi>ξ</mi></msub><mfenced><mi>ω</mi></mfenced><mo>:</mo><mo>=</mo><msub><mi>F</mi><mi>ξ</mi></msub><mfenced><mi>ω</mi></mfenced></mrow></math><img file="EP2359366B1_D0015.tif" /></maths> for ω ≥ 0 and <maths id="math0016"><math display="block"><mrow><msub><mi mathvariant="normal">Φ</mi><mi>ξ</mi></msub><mfenced><mi>ω</mi></mfenced><mo>:</mo><mo>=</mo><msub><mi mathvariant="normal">Ψ</mi><mi>ξ</mi></msub><mfenced><mi>ω</mi></mfenced><mo>:</mo><mo>≡</mo><mn>0</mn><mo>∀</mo><mi>ω</mi><mo>&lt;</mo><mn>0</mn></mrow></math><img file="EP2359366B1_D0016.tif" /></maths>

0116In the time domain a Hilbert transformation 906 of the input audio signal f 102 for generating an analytical signal 908 is done first. <maths id="math0017"><math display="block"><mrow><mi>ϕ</mi><mo>:</mo><mo>=</mo><mi>f</mi><mo>+</mo><mi>j</mi><mi mathvariant="script">H</mi><mfenced><mi>f</mi></mfenced></mrow></math><img file="EP2359366B1_D0017.tif" /></maths> and <maths id="math0018"><math display="block"><mrow><msub><mi>ϕ</mi><mrow><msub><mi mathvariant="italic">LF</mi><mi>k</mi></msub></mrow></msub><mo>=</mo><msub><mi>f</mi><mrow><msub><mi mathvariant="italic">LF</mi><mi>k</mi></msub></mrow></msub><mo>+</mo><mi>j</mi><mi mathvariant="script">H</mi><mfenced><msub><mi>f</mi><mrow><msub><mi mathvariant="italic">LF</mi><mi>k</mi></msub></mrow></msub></mfenced></mrow></math><img file="EP2359366B1_D0018.tif" /></maths> then the analytical signal <i>ϕ_{LF<sub2>k</sub2>}</i> is single side band modulated 710 with a modulator u(n) 902: <maths id="math0019"><math display="block"><mrow><mi>ψ</mi><mfenced><mi>n</mi></mfenced><mo>:</mo><mo>=</mo><mrow><mstyle displaystyle="true"><mrow><munderover><mrow><mo>∑</mo></mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>k</mi><mi>max</mi></msub></mrow></munderover></mrow></mstyle><msub><mi>ϕ</mi><mrow><msub><mi mathvariant="italic">LF</mi><mi>k</mi></msub></mrow></msub><mfenced><mi>n</mi></mfenced></mrow><mo>⋅</mo><msub><mi>μ</mi><mi>k</mi></msub><mfenced><mi>n</mi></mfenced></mrow></math><img file="EP2359366B1_D0019.tif" /></maths> or <maths id="math0020"><math display="block"><mrow><mi>ψ</mi><mfenced><mi>n</mi></mfenced><mo>:</mo><mo>=</mo><msub><mi>ϕ</mi><mi mathvariant="italic">LF</mi></msub><mfenced><mi>n</mi></mfenced><mo>⋅</mo><mi>μ</mi><mfenced><mi>n</mi></mfenced></mrow></math><img file="EP2359366B1_D0020.tif" /></maths>

0117In this way, a bandwidth extension high-frequency signal which is also called modulated signal 910 may be generated.

0118Next, a windowing (also possible with overlap) of the input signal 912 and of the extended signal 914 and a Fourier transformation 916 are performed: <maths id="math0021"><math display="block"><mrow><msub><mi>ϕ</mi><mi>ξ</mi></msub><mfenced><mi>n</mi></mfenced><mo>:</mo><mo>=</mo><msub><mi>ϕ</mi><mi mathvariant="italic">LF</mi></msub><mfenced><mi>ξ</mi><mo>⋅</mo><mfrac><mi mathvariant="italic">NFFT</mi><mn>2</mn></mfrac><mo>+</mo><mi>n</mi></mfenced></mrow></math><img file="EP2359366B1_D0021.tif" /></maths> and <maths id="math0022"><math display="block"><mrow><msub><mi>ψ</mi><mi>ξ</mi></msub><mfenced><mi>n</mi></mfenced><mo>:</mo><mo>=</mo><mi>ψ</mi><mfenced><mi>ξ</mi><mo>⋅</mo><mfrac><mi mathvariant="italic">NFFT</mi><mn>2</mn></mfrac><mo>+</mo><mi>mod</mi><mfenced separators=","><mi>n</mi><mi mathvariant="italic">NFFT</mi></mfenced><mo>+</mo><mn>1</mn></mfenced><mo>⋅</mo><mi>win</mi><mfenced><mi>mod</mi><mfenced separators=","><mi>n</mi><mi mathvariant="italic">NFFT</mi></mfenced><mo>+</mo><mn>1</mn></mfenced></mrow></math><img file="EP2359366B1_D0022.tif" /></maths> wherein an NFFT is once again the number of Fast Fourier transformation bins (for example 256, 512, 1024 bins or another number between 2⁴ and 2³²), ξ is the window number and win(.) is a window function. Thus, <maths id="math0023"><math display="inline"><mrow><mi mathvariant="normal">n</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi></mrow></math><img file="EP2359366B1_D0023.tif" /></maths> blocks 914 are created out of the original signal and in connection with that as many amplitude spectra Φ_ξ (ω), Ψ_ξ (ω) with ξ ≤ N as absolute values of the Fourier transformed 916. <maths id="math0024"><math display="block"><mrow><msub><mrow><mover><mi>γ</mi><mrow><mo>^</mo></mrow></mover></mrow><mi>k</mi></msub><mo>:</mo><mo>=</mo><mrow><mo>⌊</mo><msub><mi>γ</mi><mi>k</mi></msub><mo>⋅</mo><mi mathvariant="italic">NFFT</mi><mo>⌋</mo></mrow></mrow></math><img file="EP2359366B1_D0024.tif" /></maths> may describe the index of the band edge k in the Fourier transformed.

0119The process in the time domain is shown in <figref idref="f0009">Fig. 9</figref>.

0120The next step is the calculation 720 of the cross correlation R_ξ,k (the comparison parameter may be equal to the result of the cross correlation) of the partial amplitude spectra of the original and the extended signal which may be mathematically expressed by: <maths id="math0025"><math display="block"><mrow><msub><mi>R</mi><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mfenced><mi>ν</mi></mfenced><mo>=</mo><mrow><mo>{</mo><mtable><mtr><mtd><mfrac><mn>1</mn><mrow><msub><mrow><mover><mi>γ</mi><mrow><mo>^</mo></mrow></mover></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>−</mo><msub><mrow><mover><mi>γ</mi><mrow><mo>^</mo></mrow></mover></mrow><mi>k</mi></msub><mo>−</mo><mi>β</mi><mo>⋅</mo><mi>ν</mi><mo>+</mo><mi>δ</mi></mrow></mfrac><mrow><mstyle displaystyle="true"><mrow><munderover><mrow><mo>∑</mo></mrow><mrow><mi>ω</mi><mo>=</mo><msub><mrow><mover><mi>γ</mi><mrow><mo>^</mo></mrow></mover></mrow><mi>k</mi></msub><mo>−</mo><mmultiscripts><mrow><msub><mrow><mo>/</mo></mrow><mn>2</mn></msub></mrow><mprescripts /><none /><mi>δ</mi></mmultiscripts></mrow><mrow><msub><mrow><mover><mi>γ</mi><mrow><mo>^</mo></mrow></mover></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>+</mo><mmultiscripts><mrow><msub><mrow><mo>/</mo></mrow><mn>2</mn></msub></mrow><mprescripts /><none /><mi>δ</mi></mmultiscripts></mrow></munderover></mrow></mstyle><mrow><mfenced open="|" close="|"><msub><mi mathvariant="normal">Φ</mi><mi>ξ</mi></msub><mfenced><mi>ω</mi><mo>+</mo><mi>ν</mi></mfenced></mfenced><mo>⋅</mo><mfenced open="|" close="|"><msub><mi mathvariant="normal">Ψ</mi><mi>ξ</mi></msub><mfenced><mi>ω</mi></mfenced></mfenced></mrow></mrow></mtd><mtd><mi>ν</mi><mo>≥</mo><mn>0</mn></mtd></mtr><mtr><mtd><msub><mi>R</mi><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mfenced><mo>−</mo><mi>ν</mi></mfenced></mtd><mtd><mi>ν</mi><mo>&lt;</mo><mn>0</mn></mtd></mtr></mtable></mrow></mrow></math><img file="EP2359366B1_D0025.tif" /></maths> with <maths id="math0026"><math display="block"><mrow><msub><mi mathvariant="normal">Φ</mi><mi>ξ</mi></msub><mfenced><mi>ω</mi></mfenced><mo>:</mo><mo>≡</mo><msub><mi mathvariant="normal">Ψ</mi><mi>ξ</mi></msub><mfenced><mi>ω</mi></mfenced><mo>:</mo><mo>≡</mo><mn>0</mn><mo>∀</mo><mi>ω</mi><mo>&lt;</mo><mn>0</mn><mo>;</mo><mi>ν</mi><mo>≤</mo><mi mathvariant="normal">Λ</mi></mrow></math><img file="EP2359366B1_D0026.tif" /></maths> δ may indicate the maximum lag (the maximum offset frequency) for which a cross correlation is calculated. If the cross correlation should be calculated with a bias, i.e. small lags and thus big overlaps should be preferred, so β=0 should be selected. In contrast, if it should be compensated that fewer FFT-bins (Fast Fourier transformation bins) are overlapping for large lags than for small ones, β=1 should be chosen. In general, <maths id="math0027"><math display="inline"><mrow><mn mathvariant="normal">0</mn><mo>≤</mo><mi mathvariant="normal">β</mi><mo>∈</mo><mi mathvariant="double-struck">R</mi></mrow></math><img file="EP2359366B1_D0027.tif" /></maths> can be chosen arbitrarily. Alternatively or additionally, <maths id="math0028"><math display="inline"><mrow><mn>2</mn><mo>&lt;</mo><mi>δ</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi><mo>;</mo><mi>mod</mi><mfenced separators=","><mi>δ</mi><mn>2</mn></mfenced><mo>=</mo><mn>0</mn></mrow></math><img file="EP2359366B1_D0028.tif" /></maths> can be chosen for selecting a region of the cross correlation which is a little larger than a patch. With this the region which is considered by the cross correlation may be extended by <maths id="math0029"><math display="inline"><mrow><mfrac><mi>δ</mi><mn>2</mn></mfrac></mrow></math><img file="EP2359366B1_D0029.tif" /></maths> at both spectral ends of the particular patch.

0121Based on these results of the cross correlation, a maximum of the cross correlation 730 <maths id="math0030"><math display="block"><mrow><msub><mi>m</mi><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>:</mo><mo>=</mo><munder><mi>max</mi><mi>ν</mi></munder><mfenced><msub><mi>R</mi><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mfenced><mi>ν</mi></mfenced></mfenced></mrow></math><img file="EP2359366B1_D0030.tif" /></maths> and the lag d_ξ,k of the maximum correlation <maths id="math0031"><math display="block"><mrow><msub><mi>R</mi><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mfenced><msub><mi>d</mi><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub></mfenced><mo>=</mo><msub><mi>m</mi><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub></mrow></math><img file="EP2359366B1_D0031.tif" /></maths> may be determined.

0122Additionally, the ratios 920 of the energies or powers in the patches may be determined by the power density spectra: <maths id="math0032"><math display="block"><mrow><msub><mi>C</mi><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>:</mo><mo>=</mo><msqrt><mrow><mfrac><mrow><mstyle displaystyle="true"><mrow><munderover><mrow><mo>∑</mo></mrow><mrow><mi>ω</mi><mo>=</mo><msub><mrow><mover><mi>γ</mi><mrow><mo>^</mo></mrow></mover></mrow><mi>k</mi></msub></mrow><mrow><msub><mrow><mover><mi>γ</mi><mrow><mo>^</mo></mrow></mover></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></munderover></mrow></mstyle><mrow><msup><mfenced open="|" close="|"><msub><mi mathvariant="normal">Φ</mi><mi>ξ</mi></msub><mfenced><mi>ω</mi></mfenced></mfenced><mn>2</mn></msup></mrow></mrow><mrow><mstyle displaystyle="true"><mrow><munderover><mrow><mo>∑</mo></mrow><mrow><mi>ω</mi><mo>=</mo><msub><mrow><mover><mi>γ</mi><mrow><mo>^</mo></mrow></mover></mrow><mi>k</mi></msub></mrow><mrow><msub><mrow><mover><mi>γ</mi><mrow><mo>^</mo></mrow></mover></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></munderover></mrow></mstyle><mrow><msup><mfenced open="|" close="|"><msub><mi mathvariant="normal">Ψ</mi><mi>ξ</mi></msub><mfenced><mi>ω</mi></mfenced></mfenced><mn>2</mn></msup></mrow></mrow></mfrac></mrow></msqrt></mrow></math><img file="EP2359366B1_D0032.tif" /></maths>

0123If no clear maximum can be determined 924, the lag is put back to 0 (as shown at reference numeral 922). Otherwise the estimated lag 918 may the lag corresponding to the maximum cross correlation. For this, a suitable threshold criterion, d_ξ,k > τ with τ to be selected may be determined. Alternatively, the curvature or a spectral flatness (SFN) of the cross correlation R_ξ,k may be observed, for example: <maths id="math0033"><math display="block"><mrow><mfrac><mrow><msub><mrow><msup><mi>R</mi><mi>ʺ</mi></msup></mrow><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mfenced><mi>ν</mi></mfenced></mrow><mrow><msup><mfenced><mn>1</mn><mo>+</mo><msup><mfenced><msub><mrow><msup><mi>R</mi><mi>ʹ</mi></msup></mrow><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mfenced><mi>ν</mi></mfenced></mfenced><mn>2</mn></msup></mfenced><mrow><mmultiscripts><mrow><msub><mrow><mo>/</mo></mrow><mn>2</mn></msub></mrow><mprescripts /><none /><mn>3</mn></mmultiscripts></mrow></msup></mrow></mfrac><mo>></mo><mi>τ</mi><mo>;</mo><mfenced open="|" close="|"><mi>ν</mi></mfenced><mo>≤</mo><mi mathvariant="normal">Λ</mi></mrow></math><img file="EP2359366B1_D0033.tif" /></maths> or <maths id="math0034"><math display="block"><mrow><mfrac><mrow><mfrac><mn>1</mn><mrow><mn>2</mn><mi mathvariant="normal">Λ</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mrow><mstyle displaystyle="true"><mrow><munderover><mrow><mo>∑</mo></mrow><mi>ν</mi><mrow><mn>2</mn><mi mathvariant="normal">Λ</mi><mo>+</mo><mn>1</mn></mrow></munderover></mrow></mstyle><mrow><msub><mi>R</mi><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mfenced><mi>ν</mi></mfenced></mrow></mrow></mrow><mrow><mroot><mrow><mstyle displaystyle="true"><mrow><munderover><mrow><mo>∏</mo></mrow><mrow><mi>ν</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi mathvariant="normal">Λ</mi><mo>+</mo></mrow></munderover></mrow></mstyle><msub><mi>R</mi><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mfenced><mi>ν</mi></mfenced></mrow><mrow><mn>2</mn><mi mathvariant="normal">Λ</mi><mo>+</mo><mn>1</mn></mrow></mroot></mrow></mfrac><mo>></mo><mi>τ</mi><mn>.</mn></mrow></math><img file="EP2359366B1_D0034.tif" /></maths>

0124With <maths id="math0035"><math display="block"><mrow><msub><mrow><msup><mi>R</mi><mi>ʹ</mi></msup></mrow><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mfenced><mi>ν</mi></mfenced><mo>:</mo><mo>=</mo><mrow><mfrac><mrow><mo>∂</mo><msub><mi>R</mi><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mfenced><mi>ν</mi></mfenced></mrow><mrow><mo>∂</mo><mi>ν</mi></mrow></mfrac></mrow><mo>;</mo><msub><mrow><msup><mi>R</mi><mi>ʺ</mi></msup></mrow><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mfenced><mi>ν</mi></mfenced><mo>:</mo><mo>=</mo><mfrac><mrow><mo>∂</mo><msub><mrow><msup><mi>R</mi><mi>ʹ</mi></msup></mrow><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mfenced><mi>ν</mi></mfenced></mrow><mrow><mo>∂</mo><mi>ν</mi></mrow></mfrac></mrow></math><img file="EP2359366B1_D0035.tif" /></maths>

0125The lags d_ξ,k and the power density parameters ζ_ξ,k may be interpolated 926 to obtain a value for each time step: <maths id="math0036"><math display="block"><mrow><msub><mi>ς</mi><mi>k</mi></msub><mfenced><mi>n</mi></mfenced><mo>:</mo><mo>=</mo><mi>interp</mi><mfenced><msub><mi mathvariant="normal">C</mi><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub></mfenced><mo>;</mo><msub><mi>λ</mi><mi>k</mi></msub><mfenced><mi>n</mi></mfenced><mo>=</mo><mi>interp</mi><mfenced><msub><mi>d</mi><mrow><mi>ξ</mi><mo>,</mo><mi>k</mi></mrow></msub></mfenced></mrow></math><img file="EP2359366B1_D0036.tif" /></maths>

0126Then, the modified, amplitude modulated and frequency shifted overall modulation function may be generated: <maths id="math0037"><math display="block"><mrow><msub><mrow><mover><mi>μ</mi><mrow><mo>˜</mo></mrow></mover></mrow><mi>k</mi></msub><mfenced><mi>n</mi></mfenced><mo>=</mo><msub><mi>ς</mi><mi>k</mi></msub><mfenced><mi>n</mi></mfenced><msup><mi>e</mi><mrow><mn>2</mn><mi mathvariant="italic">πj</mi><mrow><mstyle displaystyle="true"><mrow><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover></mrow></mstyle><mrow><mfenced><msub><mi>γ</mi><mi>k</mi></msub><mfenced><mi>m</mi></mfenced><mo>+</mo><msub><mi>λ</mi><mi>k</mi></msub><mfenced><mi>m</mi></mfenced></mfenced></mrow></mrow></mrow></msup></mrow></math><img file="EP2359366B1_D0037.tif" /></maths><maths id="math0038"><math display="block"><mrow><msub><mrow><mover><mi>μ</mi><mrow><mo>˜</mo></mrow></mover></mrow><mi>k</mi></msub><mfenced><mi>n</mi></mfenced><mo>=</mo><mrow><mstyle displaystyle="true"><mrow><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>k</mi><mi>max</mi></msub></mrow></munderover></mrow></mstyle><mrow><msub><mi>ς</mi><mi>k</mi></msub><mfenced><mi>n</mi></mfenced><msup><mi>e</mi><mrow><mn>2</mn><mi mathvariant="italic">πj</mi><mrow><mstyle displaystyle="true"><mrow><munderover><mrow><mo>∑</mo></mrow><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover></mrow></mstyle><mfenced><msub><mi>γ</mi><mi>k</mi></msub><mfenced><mi>m</mi></mfenced><mo>+</mo><msub><mi>λ</mi><mi>k</mi></msub><mfenced><mi>m</mi></mfenced></mfenced></mrow></mrow></msup></mrow></mrow></mrow></math><img file="EP2359366B1_D0038.tif" /></maths>

0127This overall modulation function or the parameters of the overall modulation function may be provided 740 with the output signal for storage or transmission.

0128Additionally, further parameters for noise correction and/or tonality correction may be determined.

0129The modulation at the decoder may be done by: <maths id="math0039"><math display="block"><mrow><mover><mi>ψ</mi><mrow><mo>˜</mo></mrow></mover><mfenced><mi>n</mi></mfenced><mo>:</mo><mo>=</mo><msub><mi>ϕ</mi><mi mathvariant="italic">LF</mi></msub><mfenced><mi>n</mi></mfenced><mo>⋅</mo><mover><mi>μ</mi><mrow><mo>˜</mo></mrow></mover><mfenced><mi>n</mi></mfenced></mrow></math><img file="EP2359366B1_D0039.tif" /></maths> and addition of the k partial modulations (if there is more than one patch). For this the overall modulation function µ_k (n) or µ (n) or the parameters ζ_k (n) and λ_k (n) or c_ξ,k and d_ξ,k of the overall modulation function may be suitable coded, for example, by quantization. Optionally, the sampling rate may be reduced and a hysteresis my be introduced.

0130The calculation of the lags can be omitted, if no tonal signal is there, for example at silence, transients or noise. In these cases the lag may be set to zero.

0131<figref idref="f0011">Fig. 10</figref> shows in more detail an example 1000 for determining the lag.

0132For a time frame or window ξ=i 1010 the lag ν is set to minus λ as start value. Then the cross correlation R_ξ,k(ν) is calculated 720. If ν is smaller than Λ 1030, then ν is increased 1032 and the next comparison parameter in terms of the cross correlation is calculated 720. If ν is equal or larger than Λ 1030, then the lag corresponding to the maximum calculated cross correlation may be determined 730. If the maximum is clearly identifiable 924 the determined lag is used as parameter d_ξ,k 918. Otherwise, the lag is set to 0 and used as parameter d_ξ,k=0 922.

0133Then the whole process is repeated 1040 for the next time frame ξ=ξ+1 1050. The determined lags may be interpolated 926 to obtain a parameter for each time step N.

0134The calculation of the plurality of comparison parameters, for example, the result of the cross correlation, may be done also in parallel if a plurality of comparators are used. Also, the processing of different time frames may be done in parallel, if the necessary hardware is available several times. The loop for calculating the cross correlation may also start at +Λ and may be decreased each loop until ν ≤ Λ.

0135<figref idref="f0012">Fig. 11</figref> shows a schematic illustration of the interpolation 926 of the offset frequencies of different time frames, time intervals or windows. <figref idref="f0012">Fig. 11a</figref> shows the interpolation 1100, if the time frames do not overlap. A lag d_ξ,k is determined for a whole time frame 1110. The easiest way for interpolating a parameter for each time step 1120 may be realized by setting the parameters of all time steps 1120 of a time frame 1110 equal to the corresponding lag d_ξ,k. At the edges of a time frame the lag of the previous or the following time frame may be selected. For example, the parameters λ_k(n) to λ_k(n+3) are equal to d_ξ,k and the parameters λ_k(n+4) to λ_k(n+7) are equal to d_ξ+1,k.

0136Alternatively, the lags of the time frames 1110 may be interpolated linearly between the time frames. For example: <maths id="math0040"><math display="block"><mrow><msub><mi>λ</mi><mi>k</mi></msub><mfenced><mi>n</mi></mfenced><mo>=</mo><mfrac><mrow><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>−</mo><mn>1</mn><mo>,</mo><mi>k</mi></mrow></msub></mrow><mn>2</mn></mfrac></mrow></math><img file="EP2359366B1_D0040.tif" /></maths><maths id="math0041"><math display="block"><mrow><msub><mi>λ</mi><mi>k</mi></msub><mfenced><mi>n</mi><mo>+</mo><mn>1</mn></mfenced><mo>=</mo><mfrac><mrow><mn>3</mn><mo>⋅</mo><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>−</mo><mn>1</mn><mo>,</mo><mi>k</mi></mrow></msub></mrow><mn>4</mn></mfrac></mrow></math><img file="EP2359366B1_D0041.tif" /></maths><maths id="math0042"><math display="block"><mrow><msub><mi>λ</mi><mi>k</mi></msub><mfenced><mi>n</mi><mo>+</mo><mn>2</mn></mfenced><mo>=</mo><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>,</mo><mi>k</mi></mrow></msub></mrow></math><img file="EP2359366B1_D0042.tif" /></maths><maths id="math0043"><math display="block"><mrow><msub><mi>λ</mi><mi>k</mi></msub><mfenced><mi>n</mi><mo>+</mo><mn>3</mn></mfenced><mo>=</mo><mfrac><mrow><mn>3</mn><mo>⋅</mo><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>k</mi></mrow></msub></mrow><mn>4</mn></mfrac></mrow></math><img file="EP2359366B1_D0043.tif" /></maths><maths id="math0044"><math display="block"><mrow><msub><mi>λ</mi><mi>k</mi></msub><mfenced><mi>n</mi><mo>+</mo><mn>4</mn></mfenced><mo>=</mo><mfrac><mrow><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>k</mi></mrow></msub></mrow><mn>2</mn></mfrac></mrow></math><img file="EP2359366B1_D0044.tif" /></maths>

0137Fittingly, <figref idref="f0012">Fig. 11B</figref> shows an example 1150 for overlapping time frames 1110. In this case, one time step 1120 is associated to more than one time frame 1110. Therefore, more than one determined lag may be associated with one time step 1120. So, the determined lags may be interpolated 926 to obtain one parameter for each time step 1120. For example, the determined lags corresponding to one time step 1120 may be linearly interpolated. For example, a possible interpolation may be: <maths id="math0045"><math display="block"><mrow><msub><mi>λ</mi><mi>k</mi></msub><mfenced><mi>n</mi></mfenced><mo>=</mo><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>−</mo><mn>1</mn><mo>,</mo><mi>k</mi></mrow></msub></mrow></math><img file="EP2359366B1_D0045.tif" /></maths><maths id="math0046"><math display="block"><mrow><msub><mi>λ</mi><mi>k</mi></msub><mfenced><mi>n</mi><mo>+</mo><mn>1</mn></mfenced><mo>=</mo><mfrac><mrow><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>−</mo><mn>1</mn><mo>,</mo><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>,</mo><mi>k</mi></mrow></msub></mrow><mn>2</mn></mfrac></mrow></math><img file="EP2359366B1_D0046.tif" /></maths><maths id="math0047"><math display="block"><mrow><msub><mi>λ</mi><mi>k</mi></msub><mfenced><mi>n</mi><mo>+</mo><mn>2</mn></mfenced><mo>=</mo><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>,</mo><mi>k</mi></mrow></msub></mrow></math><img file="EP2359366B1_D0047.tif" /></maths><maths id="math0048"><math display="block"><mrow><msub><mi>λ</mi><mi>k</mi></msub><mfenced><mi>n</mi><mo>+</mo><mn>3</mn></mfenced><mo>=</mo><mfrac><mrow><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>d</mi><mrow><mi mathvariant="normal">ξ</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>k</mi></mrow></msub></mrow><mn>2</mn></mfrac></mrow></math><img file="EP2359366B1_D0048.tif" /></maths>

0138Alternatively, the interpolation may also be done, for example, by a median filtering.

0139The interpolation may be done by an interpolation means. The interpolation means may be part of the parameter extraction unit or the output interface or may be an separate unit.

0140At the decoder side the bandwidth extension may be done by: <maths id="math0049"><math display="block"><mrow><mover><mi>ψ</mi><mrow><mo>˜</mo></mrow></mover><mfenced><mi>n</mi></mfenced><mo>:</mo><mo>=</mo><msub><mi>ϕ</mi><mi mathvariant="italic">LF</mi></msub><mfenced><mi>n</mi></mfenced><mo>⋅</mo><mover><mi>μ</mi><mrow><mo>˜</mo></mrow></mover><mfenced><mi>n</mi></mfenced></mrow></math><img file="EP2359366B1_D0049.tif" /></maths>

0141After decoding of µ̃(<i>n</i>) and ϕ_LF(N) as output of the core coder. Additionally, ψ̃(<i>n</i>) may be adapted with the previously from the original signal obtained parameters for tonality and/or noise level.

0142The calculation of the overall modulation function at the decoder is done according to one of the both following formulas: <maths id="math0050"><math display="block"><mrow><mi>ψ</mi><mfenced><mi>n</mi></mfenced><mo>=</mo><mrow><mstyle displaystyle="true"><mrow><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>k</mi><mi>max</mi></msub></mrow></munderover></mrow></mstyle><mrow><msub><mi>ϕ</mi><mrow><msub><mi mathvariant="italic">LF</mi><mi>k</mi></msub></mrow></msub></mrow></mrow><mfenced><mi>n</mi></mfenced><mo>⋅</mo><msub><mi>μ</mi><mi>k</mi></msub><mfenced><mi>n</mi></mfenced><mo>+</mo><mi>noise</mi><mfenced><mi>n</mi></mfenced></mrow></math><img file="EP2359366B1_D0050.tif" /></maths> and <maths id="math0051"><math display="block"><mrow><mi>ψ</mi><mfenced><mi>n</mi></mfenced><mo>=</mo><msub><mi>ϕ</mi><mi mathvariant="italic">LF</mi></msub><mfenced><mi>n</mi></mfenced><mo>⋅</mo><mi>μ</mi><mfenced><mi>n</mi></mfenced><mo>+</mo><mi>noise</mi><mfenced><mi>n</mi></mfenced></mrow></math><img file="EP2359366B1_D0051.tif" /></maths>

0143The imaginary part of the signal may be ignored: <maths id="math0052"><math display="block"><mrow><mi>o</mi><mfenced><mi>n</mi></mfenced><mo>=</mo><mi>Re</mi><mfenced><mi>ψ</mi><mfenced><mi>n</mi></mfenced></mfenced></mrow></math><img file="EP2359366B1_D0052.tif" /></maths>

0144Then, as mentioned before, a tonality correction, for example, by inverse filtering, may follow.

0145<figref idref="f0013">Fig. 12</figref> shows a block diagram of a bandwidth extension decoder 1200 for providing a bandwidth extended audio signal 532 based on an input audio signal 502 according to an embodiment of the invention. The bandwidth extension decoder 1200 comprises a patch generator 1210, a comparator 1220, a combiner 1230 and an output interface 1240. The patch generator 1210 is connected to the comparator 1220, the comparator 1220 is connected to the combiner 1230 and the combiner 1230 is connected to the output interface 1240.

0146The patch generator 1210 generates at least one bandwidth extension high-frequency signal 1212 comprising a high-frequency band based on the input audio signal 502, wherein a lower cutoff frequency of the high-frequency band of a bandwidth extension high-frequency signal 1212 is lower than an upper cutoff frequency of the input audio signal 502. Different bandwidth extension high-frequency signals 1212 comprise different frequencies within their high-frequency bands, if different bandwidth extension high-frequency signals 1212 are generated.

0147The comparator 1220 calculates a plurality of comparison parameters. A comparison parameter is calculated based on a comparison of the input audio signal 502 and a generated bandwidth extension high-frequency signal 1212. Each comparison parameter of the plurality of comparison parameters is calculated based on a different offset frequency between the input audio signal 502 and a generated bandwidth extension high-frequency signal 1212. Further, the comparator determines a comparison parameter from the plurality of comparison parameters, wherein the determined comparison parameter fulfills a predefined criterion.

0148A combiner 1230 combines the input audio signal 502 and the bandwidth extension high-frequency signal 1212 to obtain the bandwidth extended audio signal 532, wherein the bandwidth extension high-frequency signal 1212 is based on an offset frequency corresponding to the determined comparison parameter.

0149The output interface 1240 provides the bandwidth extended audio signal 532.

0150In comparison to the decoder shown in <figref idref="f0005">Fig. 5</figref> the described decoder 1200 determines the offset frequency by itself. Therefore, it is not necessary to receive this parameter with the input audio signal 502. In this way the bit rate for transmission or storage of audio signals may be further reduced.

0151As it was described for <figref idref="f0001">Fig. 1</figref>, the patch generator 1210 may generate a plurality of bandwidth extension high-frequency signals with different offset frequencies or only one bandwidth extension high-frequency signal which is shifted by different offset frequencies. Again, also a combination of these two possibilities may be used.

0152<figref idref="f0014">Fig. 13</figref> shows a flowchart of a method 1300 for providing a bandwidth extended audio signal according to an embodiment of the invention. The method 1300 comprises generating 1310 at least one bandwidth extension high-frequency signal, calculating 1320 a plurality of comparison parameters, determining 1330 a comparison parameter from the plurality of comparison parameters, combining 1340 the input audio signal and a bandwidth extension high-frequency signal and providing 1350 the bandwidth extended audio signal.

0153A bandwidth extended high-frequency signal comprises a high-frequency band based on the input audio signal. A lower cutoff frequency of the high-frequency band of a bandwidth extended high-frequency signal is lower than an upper cutoff frequency of the input audio signal. Different bandwidth extension high-frequency signals comprise different frequencies within their high-frequency bands, if different bandwidth extension high-frequency signals are generated.

0154A comparison parameter is calculated based on the comparison of the input audio signal and the generated bandwidth extension high-frequency signal. Each comparison parameter of the plurality of comparison parameters is calculated based on a different offset frequency between the input audio signal and the generated bandwidth extension high-frequency signal.

0155The determined comparison parameter fulfills a predefined criterion.

0156The bandwidth extension high-frequency signal which is combined with the input audio signal to obtain the bandwidth audio signal is based on an offset frequency corresponding to the determined comparison parameter.

0157<figref idref="f0015">Fig. 14</figref> shows a flowchart of a method 1400 for providing a bandwidth extended audio signal according to an embodiment of the invention.

0158After receiving 1402 a bit stream comprising the input audio signal a core decoder decodes 1410 the input audio signal. Based on the input audio signal a bandwidth extension high-frequency signal is generated 1310 and the plurality of comparison parameters in terms of a cross correlation between the input audio signal and a generated bandwidth extension high-frequency signal with different offset frequencies are calculated 1320. Then, the comparison parameter fulfilling the predefined criterion is determined 1330 which is also called lag estimation.

0159Based on the offset frequency corresponding to the determined comparison parameter a modulator may modulate 1420 the input audio signal. Additionally, a parameter may be extracted 1430 from the received bit stream 1402 to adapt, for example, the power density of the modulated signal. The modulated signal is then combined 1340 with the input audio signal. Additionally, the tonality and the noise of the bandwidth extended audio signal may be corrected 1440. This may also be done before the combination with the input audio signal. Then the audio data in terms of the bandwidth extended audio signal is provided 1350, for example, for acoustic reproduction.

0160In this way, the calculation of the time variable modulation is done at the decoder side.

0161Alternatively to the modulator modulating 1420 the input audio signal to generate a patch, for example, the already previously generated bandwidth extension high-frequency signal may be used or the patch generator may generate a bandwidth extension high-frequency signal (patch) based on the offset frequency corresponding to the determined comparison parameter.

0162In other words, if low data rate is more important than a low complexity of the decoder side, the determination of the frequency modulation of the modulators may also be done at the decoder side. For this the algorithm shown in <figref idref="f0009">Fig. 9</figref> may be executed at the decoder with only some changes. Since the original signal is not available for the calculation of the cross correlation at the decoder, the correlations may be calculated between the original signal (input audio signal) and a shifted original signal (input audio signal) within an overlapping range. For example, the signal may be shifted between zero and α_k, for example, α_k divided by 2, α_k divided by 3, or α_k divided by 4. α_k indicates again the k-th band edge, for example, α₁ indicates the crossover frequency of the core coder.

0163For example, this may happen in the same way at the encoder as at the decoder. At the encoder the parameters for spectral forming, noise correction and/or tonality correction may be extracted and transmitted to the decoder.

0164Fittingly, <figref idref="f0016">Fig. 15</figref> shows a block diagram of an bandwidth extension encoder 1500 for providing an output signal using an input audio signal. The encoder 1500 corresponds to the encoder shown in <figref idref="f0004">Fig. 4</figref>. However, the encoder 1500 does not provide the output signal 132 with a parameter indication based on the offset frequency itself. It may only determine a power density parameter and optional parameters for tonality correction and noise correction and includes a parameter indication of these parameters to the output signal 132. However, the power density parameter (and also the other parameters, if they are determined) is determined based on the offset frequency corresponding to the determined comparison parameter.

0165For example, the power density parameter may indicate a ratio between the input audio signal 102 and the bandwidth extension high-frequency signal with an offset frequency corresponding to the determined comparison parameter. Therefore, the parameter indication which is related to the power density parameter and optional to the parameters for tonality correction and/or noise correction is based on the offset frequency corresponding to the determined comparison parameter.

0166A further difference between the encoder 1500 and the encoder shown in <figref idref="f0004">Fig. 4</figref> is that the patch generator 110 generates a bandwidth extension high-frequency signal in the same way the patch generator of the decoder 1400 does it. In this way the encoder 1500 and a decoder may obtain the same offset frequencies and therefore the parameters extracted by the encoder 1500 are valid for the patches generated by the decoder.

0167A device and a method for bandwidth extension of audio signals in the time domain may use time variable modulators. In other words. A patch may be generated with varying cutoff frequency, for example, for each time step, each time frame, a part of a time frame or for groups of time frames.

0168The described method for extension of the bandwidth of an audio signal can be used at the encoder side and the decoder side as well as only at the decoder side. In contrast to known methods, the described new method may carry out a so-called harmonic extension of the bandwidth without the need of exact information about the fundamental frequency of the audio signal. Further, in contrast to so-called harmonic bandwidth extensions as, for example, shown by the US provisional patent application "<patcit id="pcit0008" dnum="US61025129A" dnum-type="L"><text>F.Nagel, S. Disch: "Apparatus and method of harmonic bandwidth extension in audio signals"" with the application number US 61/025129</text></patcit> which are done by means of phase vocoders, the spectrum may not be spread and, therefore, also the density may not be changed. To ensure the harmony, correlations between the extended and the base band are exploited. This correlation can be calculated at the encoder as well as at the decoder, depending on the demand for computing and memory complexity and data rate.

0169For example, the bandwidth extension itself may be done by using an amplitude modulation (AM) and a frequency shift by means of a single side band modulation (SSB) with a plurality of slow, single adaptive, time variable carriers. A following post-processing in accordance with additional parameters may try to approximate the spectral envelope and the noise level as well as other properties of the original signals.

0170The new method for transformation of signals may avoid the problems which appear due to a simply copy or mirror operation by a harmonic correct continuation of the spectrum by means of a time variable cutoff frequency XOver between the low frequency (LF) and high-frequency (HF) region as well as between the following high-frequency regions, the so-called patches. These cutoff frequencies are chosen so that the generated patches fit an existing harmonic raster as it was existent in the original as good as possible.

0171<figref idref="f0017">Fig. 16</figref> shows a modulator with 3 time variable amplitudes and cutoff frequencies by which 3 patches can be generated by single side band modulation of the base bands. <figref idref="f0017">Fig. 16a</figref> shows a diagram 1600a of the spectrum of the bandwidth extended signal using time variable cutoff frequencies 1610. <figref idref="f0017">Fig. 16b</figref> illustrates a diagram 1600b of the spectrum of the audio signal of the three tones. In comparison to the spectrogram depicted in <figref idref="f0019">Fig. 18b</figref> the lines 1620 are significantly less smeared.

0172<figref idref="f0018">Fig. 17</figref> illustrates the effect by means of a diagram 1700 of the period. The power density spectrum of the third tones of the audio signal are shown as original 1710, with a constant cutoff frequency 1720 and with a variable cutoff frequency 1730. In contrast to using the constant cutoff frequency 1720, the harmonic structure remains by using the variable cutoff frequency 1730.

0173By the harmonic continuation of the spectrum, problems at the transition points between both, the base band (core coder) and the extended band, and between succeeding patches may be avoided. Without a F₀-estimation as requirement for the function of the system, arbitrary signals may be harmonic continued, without the existence of audible artefacts, neither by violating the harmony nor by transient sound events.

0174Some embodiments according to the invention relate to a method suitable for all audio applications, where the full bandwidth is not available. For example, for the broadcast of audio contents as, for example, with digital radio, internet stream or at audio communication applications, the described method may be used.

0175An embodiment according to the invention relates to a bandwidth extension decoder for providing a bandwidth extended audio signal based on an input audio signal and a parameter signal, as set forth in independent claim 3.

0176Some further preferred embodiments according to the invention relate to a bandwidth extension decoder as described before, wherein the patch generator is configured to amplify or attenuate the high-frequency band of the bandwidth extension high-frequency signal by a factor equal to the value of a power density parameter or equal to the reciprocal value of the power density parameter, wherein an indication of the power density parameter is contained by the input audio signal.

0177In particular, it is pointed out that, depending on the conditions, the inventive scheme may also be implemented in software. The implementation may be on a digital storage medium, particularly a floppy disk or a CD with electronically readable control signals capable of cooperating with a programmable computer system so that the corresponding method is executed. In general, the invention thus also consists in a computer program product with a program code stored on a machine-readable carrier for performing the inventive method, when the computer program product is executed on a computer. Stated in other words, the invention may thus also be realized as a computer program with a program code for performing the method according to one of claims 11-13, when the computer program is executed on a computer.