JP3279649B2 - Filter device for band division coding - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION The present invention relates to band division coding (sub-
The present invention relates to a filter device for band coding, an image processing device including the filter device, and a method of configuring the filter device.

[0002]

BACKGROUND OF THE INVENTION Band division coding is a term for certain coding techniques that use a set of filters to decimate (divide and downsample) an input signal into several narrow bands. . These separated bands are processed separately for transmission, storage, etc. Interpolate the decimated signal during the reconstruction (synthesis) stage
After filtering, the signals are added and reproduced to obtain the original signal or a signal approximate to the original signal. Decimation refers to lowering the sampling rate (sample rate) in the filter, and interpolation refers to increasing the sampling rate in the filter. Band division coding is generally applied to the processing of audio and / or video signals.

It is needless to say that it is desirable to be able to reconstruct as good as possible. With various band division encoding devices, reconstruction close to so-called "complete reconstruction" is possible.

FIG. 1 is a block diagram showing a simple example of a filter device for band division coding. This filter device
Low-pass decimation filter (A) 12, low-pass interpolation filter (B) 14, high-pass decimation filter (C) 16, high-pass interpolation filter (D) 18, and adder 20
Consisting of The filter device 10 is for storing or transmitting 22 the received signal at half the sample rate.

FIG. 2 is a diagram showing an expansion of the apparatus of FIG. 1 in order to decimate an input signal into eight bands and store or transmit the signal. In the apparatus of FIG. 2, transmission, storage, and the like can be performed at １ ／ of the original sample rate of the input signal in each of the eight signal paths.

The mathematical requirements for "perfect reconstruction" in the filter arrangement of FIG. 1 are as follows. 1) A * B + C * D = 1 (where * is convolution (convol
ution). 2) C is the complementary filter of B and D is the complementary filter of A (ie, C and D have the same coefficient values as B and A, but the majority of each coefficient is alternately inverted) There.) 3) The convolution of A * B and C * D is divided into two (1
/ 2) must be a bandpass filter. 4) The highest bit precision should be maintained. Regarding requirement 4), as much accuracy as possible should be maintained in any practical device, within the constraints of the device. Normally, an appropriate rounding (rounding) process is performed.
Bit precision is used. It is therefore impossible to obtain absolutely perfect resolution in practical devices, usually with some rounding effect. here,
The term "full resolution" is used in its ordinary technical sense. That is, considering the limitations of the actual device, the word "perfect" is never used to mean absolute.

[0007] The definition of a completely reconstructed filter pair used for band division coding is as follows. "First filter F
Given the first and second filters F2, the product of their frequency responses is a 1/2 band filter. "

When the two pairs are applied to construct a high-pass and a low-pass in a band division encoder, the following is obtained. For low pass, F1 and F1
Use 2 filters as is. For high pass
The F1 and F2 filters are deformed to bring the Nyquist to the center (no tap every other tap). The F2 filter is used for decimation and the F1 filter is used for interpolation.

The F1 and F2 filters may be interchanged as desired, but the changes must be made in both the low and high pass. That is, the F1 filter cannot be used for decimation in both the low band and the high band.

The two-divided (1/2) band-pass filter is １ ／
It indicates a response (response) of 6 dB at the Nyquist frequency, and is defined as having a symmetrical response on both sides of the 1/2 Nyquist point. According to this, a filter whose setting tap has the following shape is led (shown in FIG. 3). {F0E0D0C0BAB0C0D0E0F} (that is, all even taps except zero are 0).

As can be seen from the case where the conceptual filter F1 is convolved with itself, the result of all such convolutions is not zero at even tap positions, so that the two identical filters are 1/2. It is impossible to construct a bandpass filter. IEEE Minutes of the International Conference on Voice and Signal Processing, April 1980 (IEEE Reference No.
‥ CH1559-4 / 80 / 0000-029C198
0) pp. 291-294, “Quadratur
e) a group of filters designed for
Jay Dee Johnson outlines a filter in which the decimation filter and the interpolation filter are equal. Johnson acknowledges the existence of reconstruction errors and strives to minimize them. Another view on this problem is that there is no finite length filter with the square root response of a half band filter.

[0012] Perfect reconstruction is a desirable property, as it is to minimize as much as possible any errors in the subband encoder (although rounding or quantization errors described above). From the above discussion, it can be concluded that the prerequisite for achieving perfect reconstruction is that the decimation and interpolation filters be different.

So far, the following 2 which gives a complete reconstruction:
Two types of filters have been announced. IEEE bulletin 4 on sound, voice and signal processing issued in June 1986
In a paper entitled "Exact Reconstruction Techniques for Tree-Shaped Bandwidth Encoders" on pages 34-441, N. Smith and T. Barnwell first designed a product filter, For example, separate decomposition synthesis filter banks (terminal groups) for the minimum and maximum phase components
We propose a design method to achieve complete reconstruction by factoring into. The Smith and Barnwell method is:
It gives good filtering effect but comes with non-linear phase. Therefore, this method does not cause errors with low-level coding errors, but when distortion is introduced into the coding path, a non-linear phase error may occur, which may cause image degradation during digital video processing. is there.

[0014] IEEE Minutes of the International Conference on Voice and Signal Processing, April 1988 (IEEE Reference No.
CH2561-98880-0761, 1988)
In a paper entitled "Band Split Coding of Digital Video Using Symmetric Short Kernel Filters and Arithmetic Coding Techniques," published on pages 761 to 765, Dee Regal and A. Tabataby gave full reconstruction capabilities. Symmetric short kernel filter
A filter device that realizes a decomposition / synthesis filter bank using kernel filters is described. Regal and Tabatabay describe in their paper how to design a filter bank device that includes a symmetric short kernel FIR filter. Their design method uses a quadrature mirror (QMF) for factorizing the product filter into linear phase components.
r factorisation). However, this method is applied at a relatively simple level, with decimation and interpolation filters having slow attenuation (roll-off) characteristics and poor alias (aliasing) removal.

[0015] Our co-pending UK patent application GB
No. 9111782.0 (filed on May 31, 1991)
Also, a new type of filter has been proposed. This new type of filter is for a symmetric linear phase filter with a 帯 域 band F1 filter (ie, 6 dB at ナ イ Nyquist frequency) and a higher order matched F2 filter.

Broadly speaking, the above-mentioned Japanese Patent Application No. GB-911
No. 1782.0 proposes a filter arrangement for band division coding consisting of a first and a second filter forming a pair of matched linear phase FIR decimation and interpolation filters providing a perfect reconstruction. Things. In the filter device, the first filter is a half-band type having a predetermined integer tap coefficient, the second filter has more taps than the first filter, and the tap coefficient of the second filter is , Determined by the solution of a set of simultaneous equations derived from the zero term of the half-band filter produced by the convolution of the first and second filters. This filter device gives perfect reconstruction and linear phase.

The above-mentioned Japanese Patent Application No. GB-9111782.0 also discloses that the second filter has at least one more taps than the first filter, and the selected tap of the second filter is a predetermined half-band filter. And the remaining tap coefficients of the second filter are the solutions of a set of simultaneous equations derived from the zero term of the half-band filter produced by the convolution of the first and second filters. There is also proposed a filter device determined by: This preferred type of filter has a faster attenuation of the second filter and a correspondingly improved antialiasing.

[0018]

SUMMARY OF THE INVENTION An object of the present invention is to provide a filter device for band division coding of the type described above.
An object of the present invention is to make it possible to produce a matched second filter even when the second filter does not have a tap sum equal to a power of 2 at a higher order than the first filter.

[0019]

SUMMARY OF THE INVENTION According to a first aspect of the invention, a pair of matched linear phases F which provide perfect reconstruction.
A filter device for band division coding comprising first and second filters forming an IR decimation and interpolation filter is provided. In this filter device, the first filter has two predetermined integer tap coefficients.
Of the split (1/2) band type, the second filter has at least one more tap than the first filter, and the tap coefficients of the second filter are the convolutions of the first and second filters. ) Is determined by solving a set of simultaneous equations derived from the zero term of the half-band filter formed by Eq. (2) and iterative testing and error processing performed by setting selected tap coefficients of the second filter; The remaining tap coefficients of the second filter are determined by solving the simultaneous equations using the set selected tap coefficients.

According to a second aspect of the present invention, there is provided a method of configuring first and second filters forming a pair of matched linear phase FIR decimation and interpolation filters for band division coding. You. In the method, the second filter has at least one more taps than the first filter. The method includes the following steps.

A) setting tap coefficients for a １ ／ band type first filter; b) convolution of the first filter with a second filter having undetermined tap coefficients.
n) deriving a set of simultaneous equations using the zero term of the 帯 域 band filter formed by: c) repeatedly solving the set of simultaneous equations to derive the tap coefficients of the second filter, where The iterative step comprises: c) (i) setting selected taps of the interpolation filter; c) (ii) solving the system of equations using the set taps thus set to the remainder of the second filter. D) setting the tap coefficients of the second filter using the result of step C.

[0022]

BRIEF DESCRIPTION OF THE DRAWINGS FIG. For a given 帯 域 band response (first) filter, there is (almost always) another (second) filter matched. As described in the above-mentioned Japanese Patent Application No. GB-9111782.0, the filter device for band division encoding designs an appropriate first filter, and calculates tap coefficients of the first filter and unknown taps of the second filter. By generating a set of simultaneous equations using the zero term of the half-band filter formed by convolution with the coefficients, and solving the simultaneous equations to derive a matched second filter, it can.

The filter described in the above-mentioned Japanese Patent Application No. GB-9111782.0 is almost similar to the filter discussed in the above-mentioned Rigaru and Tabataby papers, but is of a higher order type. In other words, they are 1
A symmetric linear phase filter with a 帯 域 band first filter (ie, 6 dB at ナ イ Nyquist frequency) and a matched second filter that produces a 帯 域 band but higher order convolution response.

A classic LGT filter pair is as follows. First filter # 2,1 Second filter # 6,2, -1 Set of taps {16,9,
0, -1 (below, the filters are all oddly symmetric and therefore only show the center and right coefficients.
The complete set of tap coefficients for the LGT filter is as follows: First set 1,2,1 Second set -1,2,6,2, -1 Convolved filter set -1,0,9,16,9,0,
-1)

As mentioned above, the disadvantages of LGT filters are:
Both filters have gradual attenuation characteristics and aliases are not well removed. It has been determined that for a given half-band first filter of a higher order than that considered by Regal and Tabataby, but of roughly the same type, there is almost always a second filter that matches this.

Using the techniques outlined above and considering a second filter that is one order higher than the first filter, a matching second filter can always be created.

As described above, the definition of the completely reconstructed filter pair for band division coding is as follows: "When the first filter F1 and the second filter F2 are given, the product of their frequency responses is divided into two (1 / 2) What becomes a bandpass filter ". Therefore, the convolut of these two filters (convolut
ion) must have a 1/2 band characteristic. This means that a set of simultaneous equations must be generated in which some of the convolution terms are zero. In order to solve the system of equations, special conditions must be satisfied which give one more equation. That is, the second filter must have a zero response at Nyquist (frequency) (thus, the sum of the alternatingly inverted taps must be zero).

Next, three examples of filter pairs designed according to this technique will be described with reference to FIG. The examples shown in FIGS. 4, 5, and 6 relate to first, fourth, and eighth order first filters having the following tap values, respectively. 16, 9, 0, -1 (Σ = 32) 4th 128,77,0, -16,0, -3 (Σ = 256) 6th 512,315,0, -79,0,26, 0, -6 (Σ = 1024) 8th order

The method of calculating the tap value of the second filter will be described in detail below, taking the fourth filter as an example. The tap value of the first filter is 16, 9, 0,-
1 and tap values of the matching second filter are A, B,
Assuming C, D, and E, the convolution shown in FIG.
Solve for B, C, D, E. From the convolution shown in FIG.
It can be seen that the following simultaneous equations hold. D = 0 16E + 9D−B = 0, ie, 16E−B = 0 9D + 16C + 9B−B = 0, ie, 16C + 8B =
0

Since the number of variables is 5 and the number of equations is 3, two more equations are required. These are obtained as follows. If E = 1, B = 16E = 16, C = −
(8/16) B = −8 When the Nyquist response is defined as 0 (that is, A−2B +
2C-2D + 2E = 0), A = 2B-2C + 2D-2E
= 32 + 16-2 = 46 The solution is A = 46, B = 16, C = -8, D = 0, E =
1 and the matched second filter response for the fourth order filter is 46,16, -8,0,1 (Σ = 64).

The sum of the tap coefficients for the second filter is 2
Note that this is a power of.

When the first filter having the tap coefficients of 16, 9, 0, -1 and the second filter having the tap coefficients of 46, 16, -8, 0, 1 are combined, a complete reconstruction pair is obtained. . However, the second filter has a disadvantage that the attenuation (roll-off) characteristic is not very fast, and the alias removal characteristic is not so good.

As described in the above-mentioned Japanese Patent Application No. GB-9111782.0, the above-mentioned technique can be similarly applied to a higher-order first filter. FIG. 5 shows the characteristics of the sixth first filter and the matched second filter produced by the above-described method. The tap values giving the frequency response of FIG. 5 are as follows. (First filter) 128, 77, 0, -16, 0, 3 (Σ =
256) (Second filter) 358, 128, -61, 0, 13, 0, -3 (Σ =
512)

FIG. 6 shows the characteristics of the eighth and first filters, the matched second filter manufactured by the above-described method, and the product thereof.
Shown in The tap values giving the frequency response of FIG. 6 are as follows. (First filter) 512, 315, 0, -79, 0, 26, 0, -6
(Σ = 1024) (Second filter) 1418, 512, -236, 0, 53, 0, -20,
0,6 (Σ = 2048)

Note that the second filter always has a sum equal to a power of two. However, using the method described above has the disadvantage that the second filter frequency response shows a poor response which causes aliasing, regardless of the order of the first filter.

[0036] The above-mentioned Japanese Patent Application No. GB-9111782.0 subsequently discloses, for certain filters, particularly the first and second filters.
The above technique is developed for a filter device having a tap group in which both filters reach a power of two. this is,
The case where the 1/2 Nyquist response to such a filter is simple, that is, when the 1/2 Nyquist response to the first filter is 0.5 and the 1/2 Nyquist response to the second filter is 1.0. It is.

However, there are filters whose 1/2 Nyquist response is not so simple, and the sum of the taps of the second filter is related to the 1/2 Nyquist response of the interpolator. The relationship is plural and depends on aspects of the second filter and the first filter.

Now, the filter tap groups 10, 4, -1
Consider a first filter with When the matching tap group is determined using the above-described technique, the tap groups 56, 25,-
A second filter with 4, -1 is obtained. That is, (first filter) 10, 4, -1 (Σ = 16) (second filter) 56, 25, -4, -1 (Σ = 96) The sum of tap coefficients of the second filter is not a power of two Please note that.

Taking the above example, 1/1 of the first filter
The response at 2 Nyquist is 3/4. Therefore, the 1/2 Nyquist response of the second filter is 2
In order to satisfy the split band response, it must be 2/3. The sum of the second filter is 96,
/ 2 Nyquist size is 64, so required 2
/ 3 response is given. This second filter, which is simply one tap more than the first filter, generally has poor response attenuation characteristics. However, as long as the technique of the above-mentioned Japanese Patent Application No. GB-9111782.0 is used, a matching second filter having a sum of tap groups not higher than the power of 2 and having an order higher than the order of the first filter by two or more is manufactured. It is impossible.

The filter device according to the present invention can be used, for example, by a first technique having tap groups 10, 4, and -1 by a technique described below.
It can be determined using a filter. Here, it is assumed that the order of the second filter is larger than the first filter by 1, 3, 5, or any odd number. If the order is even larger, the last term of the second filter will simply be equal to zero. In the example described below, a second filter whose order is larger by 5 than the first filter is considered. That is, (first filter) 10, 4, -1 (second filter) A, B, C, D, E, F, G, H

FIG. 8 shows the convolution of these first and second filters. Assuming that the zero term of the two-part band response is equal to zero and the Nyquist response is zero by the convolution process, the following equation is obtained. -G + 4H = 0 {(1) -E + 4F + 10G + 4H = 0 {(2) -C + 4D + 10E + 4F-G = 0} {(3) -A + 4B + 10C + 4D-E = 0} (4) A-2B + 2C-2D + 2E-2F + 2G-2H = 0 (5)

For the equations obtained from the convolution process, there is no single solution because there are more unknowns than the equations.
Therefore, in order to solve these equations,
Use error handling. In the above example, the process includes the following steps. H is set and G is obtained from equation (1).
F is set, and E is obtained from equation (2). A value is set for D, and the remaining equations (3) to (5) are solved.

When the solution is obtained in this way, the frequency response of the obtained filter is modeled, and its attenuation characteristic is observed to check whether it is acceptable. If the frequency response is unacceptable, change one or more variable values (eg, H, F or D) set by the user and repeat the above technique. It has been found that, while setting and iterating over one of these values, one trend that allows convergence to a particular solution of the equation is easily detected. However, it should be noted that there is not always a good solution. Also,
It is very easy to generate extremely large coefficients, but it is not suitable for practical implementation. In this regard,
The first filter is a simple fraction 1 such as 2/3, 3/4
It has been found that with a / 2 Nyquist response, the coefficients of the second filter are generally simpler. The coefficients of the second filter largely depend on the coefficients of the first filter, especially those outside it. Also, as the difference between the tap order of the second filter and the tap order of the first filter increases, it becomes increasingly difficult to find a tendency to converge to a suitable solution.

However, by using the technique described above,
Note that very useful inventive filter devices can be determined. Next, a specific example of such a filter will be described. 9 to 11 show filter response characteristics of those filters.

FIG. 9 shows the frequency response of the first filter device to the filter pair. The filters that generate their frequency response are as follows. (First filter) 10,4, -1 (−１ = 16,1 / 2 Nyquist = 0,
Nyquist = 0) (second filter) 272, 135, -20, -16, 4, 1 (１ = 48
0, 1/2 Nyquist = 320, Nyquist = 0)

FIG. 10 shows the frequency response of the second filter device to the filter pair. The filters that generate their frequency response are as follows. (First filter) 38, 18, -4, -2, 1 (Σ = 64, 1/2 Nyquist = 48, Nyquist = 0) (Second filter) 1924, 992, -140, -139, 46, 13 ,
−4, −2 (Σ = 3456, ナ イ Nyquist = 230)
4, Nyquist = 0).

FIG. 11 shows the frequency response of the third filter device to the filter pair. The filters that generate their frequency response are as follows. (First filter) 142, 76, -11, -14, 5, 2, -1 (Σ = 2
56,1 / 2 Nyquist = 176, Nyquist = 0) (Second filter) 9628,4932, -906, -779,364,8
9, −54, −21, 6, 3 (Σ = 16896, 1/2)
Nyquist = 12288, Nyquist = 0).

[0048]

The filter device according to the invention provides perfect reconstruction and linear phase and is therefore suitable for processing digital image signals. The decimation filter is
Used to store the image signal in a video storage medium for transmission or the like, the interpolation filter
It is used to reconstruct or subsequently transmit the original image signal from the storage medium.

In summary, the first filter can be easily determined by simple low-pass filter design software, -3
It has a 1/2 Nyquist response approximating to dB. The second filter also has a resulting 1 close to -3 dB.
/ 2 Nyquist response. The tap group of the second filter is preferably set to be longer than the first filter by several elements in order to improve alias removal.

Normally, the first filter is, for example, a Sony CX
It can be implemented with a single FIR digital filter chip such as a D2200 IC chip. The second filter generally requires a higher decomposition factor, which means that two CXD2200 chips are in parallel, one for lower order bits,
One can be achieved by using the higher order bits and summing the outputs with an adder. These filters are generally
Can be applied for data reduction purposes.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating a simple example of a filter device for band division encoding.

FIG. 2 is a block diagram illustrating an example of a filter device for band division coding divided into eight bands.

FIG. 3 is a curve diagram showing characteristics of a two-divided bandpass filter.

FIG. 4 is a curve diagram showing a first example of response characteristics of the first and second filters of the first type.

FIG. 5 is a curve diagram showing a second example of response characteristics of the first and second filters of the first type;

FIG. 6 is a curve diagram showing a third example of response characteristics to first and second filters of the first type and their products.

FIG. 7 is a chart for explaining creation of the first type of filter.

FIG. 8 is a table for explaining creation of a second type of filter described below.

FIG. 9 is a curve diagram showing a first example of response characteristics of the first and second filters of the second type according to the present invention.

FIG. 10 is a curve diagram showing a second example of response characteristics of the first and second filters of the second type according to the present invention.

FIG. 11 is a curve diagram showing a third example of response characteristics of the first and second filters of the second type according to the present invention.

FIG. 12 is a block diagram showing an application example of the filter device of the present invention.

[Explanation of symbols]

 12 low pass decimation filter 14 low pass interpolation filter 16 high pass decimation filter 18 high pass interpolation filter

────────────────────────────────────────────────── ─── Continuation of the front page (56) References JP-A-4-56490 (JP, A) JP-A-4-352582 (JP, A) JP-A-4-343577 (JP, A) (58) Field (Int.Cl. ⁷ , DB name) H04N 5/91-5/956 H04N ^7/ 24-7/68

Claims (9)

(57) [Claims] 1. A filter device for band division coding comprising a pair of linear phase FIR decimation filters and an interpolation filter matched to provide perfect reconstruction, comprising: One of the first filters is of a predetermined type having an integer tap coefficient, and the other of the pair of filters is a second filter having at least one more taps than the first filter. A two-part band-pass filter in which a part of the set of tap coefficients is determined by a value set by trial and error, and the remaining tap coefficients are formed by convolution of the first and second filters. Characterized by being solved by solving a set of simultaneous equations derived from the zero term of Band division encoding filter device. 2. The filter device according to claim 1, wherein a part of the set of tap coefficients is modeled when the value of the part of the tap coefficients is changed by trial and error. A filter device, wherein the setting is made based on a change appearing in a response characteristic of the second filter. 3. The filter device according to claim 1, wherein the first filter is the decimation filter, and the second filter is the interpolation filter. 4. The filter device according to claim 1, wherein the first filter is the interpolation filter, and the second filter is the decimation filter. 5. The filter device according to claim 1, wherein a pair of matched decimation filters and interpolation filters corresponding to a high frequency band, and a pair corresponding to a low frequency band. A pair of matched decimation and interpolation filters, the decimation filters corresponding to the high and low frequency bands each having an input for receiving a common stream of input samples; A filter device, wherein the interpolation filters corresponding to the band and the low-frequency band each have an output connected to a means for synthesizing signals output from these. 6. Matching 1 to give perfect reconstruction
A method of configuring a pair of linear phase FIR decimation filters and interpolation filters, wherein the second filter, which is the other of the pair of filters, includes
A filter configuration method comprising the following steps when the number of taps is at least one pair greater than the first filter that is one of a pair of filters. (A) setting tap coefficients for the first filter; (b) one set using a zero term of a two-band filter formed by convolution of the first filter with a second filter whose tap coefficients are undetermined (C) repeating the following steps (c) (i) and (c) (ii) to find a solution to the set of simultaneous equations, and a set of tap coefficients of the second filter (C) (i) setting values of some tap coefficients of the set of tap coefficients of the second filter; (c) (ii) setting of some of the set tap coefficients. Solving the simultaneous equations using tap coefficients to obtain tap coefficients of the remaining portion of the second filter; (d) using the result of the step (c) to calculate a set of tap coefficients of the second filter; To set. 7. The method according to claim 6, wherein the step (c) further includes the following step. (C) (ii
i) modeling the response characteristic of the second filter; (c) (iv) a change appearing in the response characteristic of the second filter when some of the tap coefficients for which the above values are set are varied by trial and error. To ask. 8. The filter configuration according to claim 6, wherein the first filter is the decimation filter, and the second filter is the interpolation filter. Method. 9. The filter configuration according to claim 6, wherein the first filter is the interpolation filter, and the second filter is the decimation filter. Method.