Separable diamond shaped multidimensional filters for composite video encoding/decoding applications.

BACKGROUND OF THE INVENTION

Field of the invention

0001This invention relates to an apparatus for encoding/decoding a composite color video signal and more particularly, to a multidimensional filter for the separation of the luminance and chrominance components of NTSC, PAL and ATV color television signals. The present invention also relates to a method for designing several classes of diamond shaped filter.

Description of the Prior Art

0002During the past few years, there has been an increasing use of vertical delay line comb filters for improving the horizontal separation of the luminance and chrominance composents in a composite TV signal. Several separable filters respectively in the horizontal and vertical domains have been implemented with analog or digital techniques as disclosed in U.S. Patents Nos. 4,345,268; 4,500,912 and 4,524.400. However, this class of filters yield a resolution loss of diagonal high frequency luminance information. Therefore, some adaptation and/or compensation techniques were suggested such as disclosed in U.S. Patent Nos. 4,040,084 and 4,240,105. However adaptation artifacts can be introduced in the viewed image.

0003Recently there was introduced the diamond shaped spectrum of the chrominance components in an NTSC encoded signal, and U.S. Patent No. 4,829,367 teaches the use of non-separable horizontal vertical diamond shaped filters for NTSC encoding and decoding. These non-separable filters are generally complex and the luminance bandstop filter performance is not ideal along the horizontal and vertical frequency domain axes.

0004In the vertical temporal domain, U.S. Patent No. 4,683,490 describes the use of diamond shaped filters implements with odd and even field delays and suitable lowpass and highpass filter coefficients. However, the proposed twelve field filter yields a limit of 15 dB for component separation along the zero axes. The inventors have also suggested the use of frame sampled filters which are simply rectangular shaped bandpass or bandstop filters in the vertical temporal frequency domain.

0005In the case of encoding/decoding a PAL video signal, the situation is quite similar. In an article by J.O. Drewery, entitled "The Filtering of Luminance and Chrominance Signals to Avoid Cross - Colour in a PAL Colour System", BBC Engineering, 8-39, Sept 1976, there is proposed some (separable) rectangular or (non-separable) circular shaped filters in the spatial frequency domain. The choice of circular shaped region remains intuitive and yields a relatively simple filter calculation. In the vertical-temporal domain. Drewery and C.K.P. Clarke, in an article entitled "PAL Decoding: Multidimensional Filter Design for Chrominance - Luminance Separation", BBC Research Department Report no BBC-RD 1988/11, have suggested also the use of odd and even field delays for diamond shaped filter implementation. The filter performance is similar to that of filter performance of U.S. Patent No. 4, 683,490, in the case of NTSC signal.

0006Finally, it is noted that all existing proposed filters have the diamond shaped region in either the horizontal-vertical or vertical-temporal domain.

SUMMARY OF INVENTION

0007It is a feature of the present invention to provide a general separable 3D diamond shaped filter in both horizontal-vertical and vertical-temporal domains for encoding/decoding an NTSC video signal. The filter includes a matching delay, an adder and the cascaded connection of seven unidimensional filters working individually in their own zero or oblique frequency axis.

0008Another feature of the present invention is to provide economical versions of diamond shaped filters in only one of the above-mentioned domains.

0009A further feature of the present invention is to provide diamond shaped filters obtained by combining separable and simple unidimensional filters.

0010A still further feature of the present invention is to provide a class of NTSC encoding/decoding filters capable of preserving the luminance information along the three zero axis in frequency domain.

0011Another feature of the present invention is to provide a diamond shaped filter in the spatial frequency domain for encoding/decoding a PAL video signal.

0012Yet another objective of the present invention is to provide a high quality but economical 3D separable filter using few field delays for encoding/decoding a PAL video signal.

0013A still further feature of the present invention is to provide several 3D diamond shaped filters allowing the use of the Fukinuki hole for ATV applications. These filters are disclosed in the article of Fukinuki, Hirano, enti- fled "Extended Definition TV Fully Compatible with existing Standard", IEEE Trans. on Communications, vol.

COM32, no. 8, August 1986, pp. 948-953.

0014According to a broad aspect of the present invention, there is provided a diamond shaped multidimensional filter circuit for decoding composite video signals. The diamond shaped filter circuit is comprised of a series configuration of separable filters connected at an input to the composition video signals. A matching delay circuit is connected to the input and provides a delayed output signal matching the delay of the resulting signal of the series of separable filters. The series configuration produce a chrominance signal at an output thereof. An adder circuit is provided and has a positive and a negative input. The negative input is connected to the chrominance output to receive the chrominance signal. The delayed output signal is connected to the positive input of the adder whereby the adder will yield a bandstop luminous signal at an output thereof.

0015According to a still further broad aspect of the present invention, there is provided a diamond shaped multidimensional filter circuit for encoding composite video signals. The diamond shaped filter circuit comprises two series configuration of separable unidimensional lowpassfilters connected respectively to two chrominance input signals and producing two lowpass chrominance input signals. A chroma quadrature modulator is connected to the lowpass chrominance output signals and provides a modulated chroma output signal. A separable diamond shaped filter is connected to a luminance input signal and produces a bandstop luminance output signal. A matching delay circuit is connected to the bandstop luminance output signal and provides a delayed luminance output signal matching the delay of the modulated chroma output signal. An adder is connected to the delayed luminance output signal and the modulated chroma output signal and produces at the output thereof a composite video signal.

0016According to a still further broad aspect of the present invention, there is provided a diamond shaped multidimensional filter circuit for encoding composite video signals. The circuit comprises a chroma quadrature modulator connected to chrominance input signals. A matching delay circuit is connected to a luminance input signal. The chroma quadrature modulator has an output connected to a negative input of a first adder circuit. The first adder circuit has a positive input connected to the luminance input signal. The adder circuit yields an output signal which is fed to a bandpass filter formed of a series connection of separable filters. The output of the bandpass filter is connected to a negative input of a second adder circuit. The delayed luminance output signal is fed to a positive input of the second adder circuit whereby the second adder circuit yields a composite video output signal.

0017According to a still further broad aspect of the present invention, there is provided a method of decoding composite video signals by the use of a diamond shaped multidimensional filter circuit. The method comprises feeding the composite video signals to an input of the series configuration of separable filters. The composite video signals are also fed to a matching delay circuit. The matching delay circuit produces a delayed video output signal which is matched to the delay caused by the series of separable filters. A chrominance signal is pro- ducedat an output of a series of separable filters to produce an output chrominance signal. The output of the separable filters is fed to an adder circuit negative input. The delayed video output signal is fed to a positive input of the adder whereby the adder will produce a bandstop luminance signal at an output thereof.

0018According to a still further broad aspect of the present invention, there is provided a method of encoding composite video signals by the use of a diamond shaped multidimensional filter circuit. The method comprises feeding chrominance input signals to two series configuration of separable unidimensional lowpass filters to produce lowpass chrominance output signals. The lowpass chrominance output signals are modulated to produce a modulated chrominance signal. A luminance input signal is fed to a series configuration of separable unidimensional filters to produce a bandpass luminance output signal and to a matching delay circuit to provide a delayed luminance output signal matching the delay of the separable series connected filters. The delayed luminance output signal and the bandpass luminance output signal are fed to a positive input and negative input, respectively, of an adder circuit to provide a bandstop luminance output signal. The bandstop luminance output signal is delay-matched to produce a delayed bandstop luminance output signal having the same delay as the modulator chroma output signal. The modulated chroma output signal and the delayed bandstop luminance output signal are fed to an adder circuit to produce at an output thereof a composite video signal.

BRIEF DESCRIPTION OF THE DRAWINGS

0019A preferred embodiment of the present invention will now be described with reference to the accompanying drawings in which:

0020<ul id="ul0001" list-style="none"><li>FIGURE 1 is a block diagram of the proposed interframe 3D diamond shaped separable bandpass-bandstop filter for NTSC encoding/decoding;</li><li>FIGURE 2 is a block diagram of the proposed spatial diamond shaped separable bandpass-bandstop filter with an optional temporal bandpass filter for NTSC encoding/decoding;</li><li>FIGURE 3 is a block diagram of the proposed NTSC interframe diamond shaped separable bandpass-bandstop filter;</li><li>FIGURE 4 is a block diagram of the proposed NTSC interfield diamond shaped separable bandpass-bandstop filter for both chroma and Fukinuki hole informations;</li><li>FIGURE 5A is a block diagram of chroma encoding lowpass filter associated with Figures. 1, 2, 3, and 4;</li><li>FIGURE 5B is a block diagram of luminance chrominance non-complementary encoding filter using the circuit of Figures 1, 2, 3, 4, and 5.</li><li>FIGURE 5C is a block diagram of a luminance chrominance complementary encoding filter with the proposed bandpass filters shown in Figures 1, 2, 3, and 4;</li><li>FIGURE 6 is a block diagram of a FIR 1 D filter which may be used in the circuit of Figures 1, 2, 3, 4, and 5;</li><li>FIGURE 7 is a perspective view of a general spatial-temporal spectrum form of the filter of Figure 1;</li><li>FIGURE 8 is a perspective view of a general spatial-temporal spectrum form of the filters of Figure 2, 3, and 4;</li><li>FIGURES 9A, B, and C illustrate as example, the spectral result of the 1 H+2P and 1 H-2P lowpass filters in series;</li><li>FIGURES 10A, B, C, and D are perspective views and graphs illustrating as example, spectral characteristics of the spatial diamond shaped filter of Figure 2;</li><li>FIGURE 11 is a block diagram of the proposed PAL 3D separable bandpass-bandstop filter;</li><li>FIGURE 12 represents the weight array notation for the two field non-separable bandpass filter 1205;</li><li>FIGURE 13 is a block diagram of the proposed spatial diamond shaped separable bandpass-bandstop filter for PAL encoding/decoding;</li><li>FIGURE 14 is a block diagram of the proposed PAL 3D bandpass-bandstop filter in which the diamond shaped feature in the spatial domain is removed;</li><li>FIGURE 15 is a block diagram of the proposed temporal-vertical completely separable diamond shaped PAL bandpass filter;</li><li>FIGURE 16 is a graph illustrating as example, spectral characteristics of the spatial diamond shaped PAL filter of Figure 13;</li><li>FIGURE 17 illustrates temporal-vertical spectral characteristics of the filter 1202 or 1502; and</li><li>FIGURE 18 represents temporal-vertical spectral characteristics of the filter 1602.</li></ul>

DESCRIPTION OF THE PREFERRED EMBODIMENTS

0021Referring now to the drawings, and more particularly to Figure 1, there is illustrated the proposed interframe 3D diamond shaped bandpass-bandstop filter of the invention for NTSC encoding and decoding. It consists generally of a matching delay 112, and adder 114 and a separable 3D diamond shaped bandpass filter. The proposed bandpass filter is composed of seven small filters in series, namely: temporal bandpass filter 103, 526 H lowpass filter 104,524 H lowpass filter 105, vertical highpass filter 106,1 H+2P lowpass filter 107, 1 H-2P lowpass filter 108 and finally horizontal bandpass or highpass filter 109. The filter position ordering is not an important factor for the system's functionality. However, in order to minimize the matching delay 112, the filter which produces the longest delay will be placed at the begining of the sequence. In the present case, there are three possible candidates: the temporal bandpass filter 103, and the 526 H or 524 H lowpass filters 104, 105, respectively. These three filters together with 106 form the diamond shaped temporal-vertical bandpass filter. The other filters 106, 107, 108, 109 form a horizontal-vertical diamond shaped filter.

0022The video input 101, orthogonally sampled at four times the color subcarrier frequency, is supplied to the first filter input. The appropriate delayed input 111 produced by the first filter is sent, in turn, to the matching delay 112. The bandpass output 110 is sent together with the matching delay output 113, respectively to the negative and positive inputs of the adder 114 which yields the bandstop luminance output 115. In the decoding case, the bandpass output 110 corresponds to the modulated chroma output.

0023Considering now, in detail, the seven filters which form the desired separable diamond shaped 3D bandpass filter. These filters are simply FIR unidimensional filters working individually in their own and appropriate dimensions. Figure 6 illustrates a finite impulse response 1 D filter and the associated delay to various types of filter. The transfer functions of the seven filters in Figure 1 are respectively: <ul id="ul0002" list-style="none"><li>The temporal band filter:<maths id="math0001" num=""><img file="EP0454591A2_D0001.tif" /></maths></li></ul>

0024The 526 H lowpass filter:<maths id="math0002" num=""><img file="EP0454591A2_D0002.tif" /></maths>

0025The 524 H lowpass filter:<maths id="math0003" num=""><img file="EP0454591A2_D0003.tif" /></maths>

0026The vertical highpass filter:<maths id="math0004" num=""><img file="EP0454591A2_D0004.tif" /></maths>

0027The 1 H+2P lowpass filter:<maths id="math0005" num=""><img file="EP0454591A2_D0005.tif" /></maths>

0028The 1 H-2P lowpass filter:<maths id="math0006" num=""><img file="EP0454591A2_D0006.tif" /></maths>

0029The horizontal bandpass filter:<maths id="math0007" num=""><img file="EP0454591A2_D0007.tif" /></maths>

0030In these above expressions, H denotes 1 line delay, P is 1 pixel delay. The normalized frequencies ω₁, ₀₂, ₀₃, respectively to the horizontal, vertical and temporal frequencies are defined as follows:<maths id="math0008" num=""><img file="EP0454591A2_D0008.tif" /></maths>in which i = 1, 2, 3 and the corresponding sampling frequencies f_si are<maths id="math0009" num=""><img file="EP0454591A2_D0009.tif" /></maths>f_s2 = 262.5 c/ph or cycle / picture height (10)<maths id="math0010" num=""><img file="EP0454591A2_D0010.tif" /></maths>

0031The pair of filters 104 and 105 yields diamond shaped in the vertical-temporal domain. In similar manner, the filters 107 and 108 form diamond regions in the horizontal-vertical domain.

0032It is worthwhile to note that similar filters with the sampling frequency SI = 13.5 MHz can be used. However, it is necessary to take some precaution in filter design about the offset between 13.5 MHz/4 and the color subcarrier frequency.

0033Figure 7 illustrates a portion of spatial-temporal spectra form of the resulting filter in Figure 1. It is pointed out that in the horizontal-temporal frequency domain the filter shape is not a diamond. This consideration is based on the true spectrum of various image sequences.

0034Moreover, by using the frame delay, the resulting bandpass-bandstop filters in Figure 1 are suitable for both chroma and Fukinuki hole informations.

0035Various filter coefficients for the configuration in Figure 1 are given in Table 1. There is a filter with 16 fields. It is noted that the filter coefficients are simple and the coefficient multiplications can be implemented using adders. <tables id="tabl0001" num="0001"><img file="EP0454591A2_D0011.tif" /></tables>

0036Referring now to Figure 2 which illustrates the simplest version of the previous filter, it is a separable diamond shaped filter working essentially in the intrafield spatial domain. The proposed bandpass filter consists of five small filters in series: optional temporal bandpass filter 203, vertical high pass filter 204, 1 H+2P lowpass filter 205, 1 H-2P lowpass filter 205 and horizontal bandpass filter 207.

0037The transfer functions of these filters are given respectively in equations (1), (4), (5), (6) and (7).

0038FIGURE 8 represents a portion of spatial-temporal spectra form of the resulting filter of Figure 2. The diamond shaped characteristic is only in the horizontal-vertical frequency domain. The optional bandpass 203 limits the filter spread in the temporal frequency domain.

0039As an example, the coefficients of a filter with 12 lines are given in Table II. The optional temporal bandpass filter coefficients are also given for completeness. An eight field filter yields good result. of course, differentfilters can be obtained according to desired specifications. <tables id="tabl0002" num="0002"><img file="EP0454591A2_D0012.tif" /></tables>

0040Figure 8 represents the spatial spectral characteristics of the filter defined by the give coefficients. It is noted that, in order to reduce the frame store memory, the optional temporal bandpass filter in Figure 2 can be designed using IIR, infinite impulse response, filter techniques.

0041Referring now to Figure 3, there is illustrated the proposed interframe separable bandpass-bandstop filter for NTSC enclding decoding. It is a simplified version of the filter of Figure 1. The bandpass filter is composed of five small filters in series: temporal bandpass filter 303, 526 H lowpass filter 304, 524 H lowpass filter 305, vertical highpass filter 306, horizontal bandpass filter 307.

0042The transfer functions of these filters are given respectively in equations (1), (2), (3), (4) and (7).

0043Figure 8 illustrates the 3D spectral characteristics of the filter of Figure 3. In this case, the diamond shaped characteristic is in the temporal-vertical frequency domain. Table 111 shows the 14 field filter coefficients as an example. <tables id="tabl0003" num="0003"><img file="EP0454591A2_D0013.tif" /></tables>

0044Referring now to Figure 4 there is illustrated the proposed NTSC interfield separable bandpass-bandstop filter for both chroma and Fukinuki hole informations. The 3D bandpass filter is composed of seven filters 403, 408, 409, 416, 417, 418, 419 and an adder 407. The video signal 401 is applied to the input of the temporal bandpass filter 403. The filter output 404 is sent, in parallel, to both filters 416, 418 followed respectively by the filters 417, 419. The respective outputs 405, 406 of the above filters are combined together to the adder 407 followed, in series, by the vertical highpass filter 408 and the horizontal bandpass filter 409. The resulting signal 410 is the 3D bandpass filter output.

0045The transfer functions of the filters 403, 408 and 409 are described respectively by equations (1), (4) and (7).

0046The 263 H filters 416 and 418 have the following expression as transfer function:<maths id="math0011" num=""><img file="EP0454591A2_D0014.tif" /></maths>

0047Finally for the 262H filters 417 and 419:<maths id="math0012" num=""><img file="EP0454591A2_D0015.tif" /></maths>

0048The diamond shaped filter region, similar to that of the previous interframe filter, is in the temporal-vertical frequency domain as illustrated by Figure 8.

0049From an encoding point of view, the Figures 1, 2, 3, and 4 are suitable only for the luminance component. Figure 5A illustrates the associated lowpass filter chroma encoding. In the complete case corresponding to Figure 1, the proposed chroma lowpass filter includes the cascade connection of seven unidimensional lowpass filters 502, 503, 504, 505, 506, 507, and 508. The transfer functions of the filters 502, 503, 504, 505, 506, and 507 are given respectively by equations (1), (12), (13), (4), (5), and 6). For the horizontal lowpass filter 508, the transfer function is described as follows:

0050<maths id="math0013" num=""><img file="EP0454591A2_D0016.tif" /></maths>

0051Associated with Figure 2, the encoding chroma lowpass filter illustrated in Figure 5A contains only five filters 502 (optional), 505, 506, 507, and 508 in series. As for the case of Figures 3 and 4, the corresponding chroma lowpass filter is composed of 502, 503, 504, 505, and 508.

0052The above described filters can be used for NTSC encoding as shown in Figures 5 and 6. Figure 5B consists of two proposed separable diamond shaped lowpass filters 520, 521, respectively for the two chroma components I and Q, a chroma quadrature modulator 522, a proposed separable diamond shaped bandstop filter 523 for the luminance component Y, a matching delay 524, and an adder 525.

0053Referring now to Figure 5C, there is shown a complementary filter for both luminance-chrominance encoding. Since this configuration is well known, it is sufficient to mention that the bandpass filter 514 is now one of the previously described bandpass filter in Figures 1, 2, 3, and 4.

0054Having described the preferred embodiments concerning NTSC encoding/decoding, we now consider the PAL video signal.

0055Referring now to Figure 11, there is shown the proposed configuration of the PAL interfield 3D separable filter which is composed of six filters 1204, 1205, 1206, 1207, 1208 and 1209. The video input 1201, quasi-orthogonally sampled at 4 f_sc is applied to the filter input. The transfer functions of the six filters in Figure 11 are given respectively as follows: <ul id="ul0003" list-style="none"><li>The horizontal bandpass filter 1209:<maths id="math0014" num=""><img file="EP0454591A2_D0017.tif" /></maths></li><li>The H-2P bandpass filter 1208:<maths id="math0015" num=""><img file="EP0454591A2_D0018.tif" /></maths></li><li>The H+2P bandpass filter 1207:<maths id="math0016" num=""><img file="EP0454591A2_D0019.tif" /></maths></li><li>The vertical bandpass filter 1206:<maths id="math0017" num=""><img file="EP0454591A2_D0020.tif" /></maths></li><li>The 313 H highpass filter 1204:<maths id="math0018" num=""><img file="EP0454591A2_D0021.tif" /></maths></li></ul>

0056The two field non separable bandpass filters 1205: <ul id="ul0004" list-style="none"><li>[C_o + 2C₁ COS (₀₃ + 1/2 ω₂) + 2C₂ COS (ω₃ - 3/2 ω₂) ⁺ 2C₃ COS 2₀₀₂⁺ 2C₄ COS (ω₃ + 5/2 ω₂) + 2C₅ COS (ω₃ - 7/2 ω₂) + 2C₆ COS 4ω₂ + ...] (20)</li></ul> in which the coefficients C_o, C_l, ... C₅ are illustrated in a weight array as shown in figure 12. The normalized frequencies ω₁, ω₂, ₀₃ respectively to the horizontal, vertical and temporal frequencies are defined as follows:<maths id="math0019" num=""><img file="EP0454591A2_D0022.tif" /></maths>in which the corresponding sampling frequencies are<maths id="math0020" num=""><img file="EP0454591A2_D0023.tif" /></maths><maths id="math0021" num=""><img file="EP0454591A2_D0024.tif" /></maths><maths id="math0022" num=""><img file="EP0454591A2_D0025.tif" /></maths>

0057It is pointed out that according to desired specifications, various filter coefficients can be obtained.

0058Various filter coefficients for the configuration in Figure 11 are given in Table IV. There are two filters using respectively 4 and 6 fields. It is interesting to note that: <ul id="ul0005" list-style="none"><li>Primo, in the temporal vertical frequency domain, the filter 1202 spectral shape, illustrated by Figure 17, is not yet a diamond. However, the shape is locally symmetrical around the subcarrier frequency center. This feature is important in a double sideband modulation system.</li></ul>

0059Secundo, the horizontal bandpass filter 1209 is lengthy, it is then desirable to decompose it in two or more small filters in series. The equation (15) becomes:<maths id="math0023" num=""><img file="EP0454591A2_D0026.tif" /></maths>The coefficients a_n and b_n are choosen as follows: <tables id="tabl0004" num="0004"><img file="EP0454591A2_D0027.tif" /></tables><tables id="tabl0005" num="0005"><img file="EP0454591A2_D0028.tif" /></tables>

0060Tertio, in order to obtain a larger chroma bandwidth the coefficients in the two filters 1207 and 1208 can be changed as follows:<maths id="math0024" num=""><img file="EP0454591A2_D0029.tif" /></maths>

0061Referring now to the drawings, Figure 13 represents a block diagram of the proposed spatial (horizontal,vertical) diamond shaped bandpass bandstop filter for PAL encoding/decoding. It contains only four filters 1409, 1408,1407,1406 in series. The corresponding transfer functions are given respectively by equations (15), (16), (17), and (18). The filter coefficients are the same given in Table IV respectively in the corresponding columns 1209, 1208, 1207 and 1206. Figure 17 illustrates the spatial spectral filter characteristics.

0062Figure 14 illustrates a block diagram of the proposed PAL 3D filter in which the diamond shaped feature in the spatial domain is removed. It contains four filters 1509, 1506, 1505 and 1504 in series. The filter transfer functions are given respectively in equations (15), (18), (20) and (19). The coefficients of the filters 1505 and 1504 can be chosen as the same given in Table IV respectively in the corresponding columns 1205 and 1204. However, the coefficients of the filter 1506 and 1509 can be obtained by any filter design program satisfying given desired specifications.

0063Figure 15 represents another proposed block diagram of the diamond shaped temporal-vertical PAL bandpass filter. It is completely separable by two 1D filters 1604, 1605 in series. The transfer function of the 313 H highpass filter 1604 is described already by equation (19). The transfer function of the 312 H bandpass filter 1605 is given as follows:<maths id="math0025" num=""><img file="EP0454591A2_D0030.tif" /></maths>Table V resumes the employed coefficients for three bandpass filters using 10, 12 and 16 fields respectively. Figure 18 illustrates the 10 field filter response in the temporal-vertical frequency domain.

0064If the diamond shaped characteristics in the temporal-vertical frequency domain is desired, at the expense of frame stores, the blocks 1202 or 1502 in Figures 11 or 14 respectively can be substituted by the 1602 in Figure 15. <tables id="tabl0006" num="0006"><img file="EP0454591A2_D0031.tif" /></tables>

0065Various diamond shaped filters are herein proposed for encoding/decoding the NTSC, PAL and ATV video signals. These filters are separable and, therefore, implemented by introducing various oblique frequency axes such as (2ω1 + ω₂, 2ω₁ - ω₂) for NTSC, PAL spatial filter, (2ω3 + ω₂, 2ω3- ω2) for interframe filter, (ω3 + <maths id="math0026" num=""><img file="EP0454591A2_D0032.tif" /></maths>ω₂, ω₃ - <maths id="math0027" num=""><img file="EP0454591A2_D0033.tif" /></maths>ω₂) for interfield filter. This can be explained briefly as follows. Let us consider, for example, the pair of 1 H+2P and 1 H-2P lowpass filters. Referring to Figure 9A, there is represented the spatial data array of a video signal. The enclosed dots correspond to sampled data stored in these filters for a given central pixel. The cascade connection of these two lowpass filters results in three pass bands in the spatial frequency domain, as illustrated by Figure 9B. In order to obtain only the desired band shown in Figure 9C, it is necessary to use a pair of horizontal bandpass and vertical highpass filters in series. The two last filters provide at a same time two main benefits for controlling the diamond shape dimensions and the desired system performance along the zero axes.