JPH07107051A - Sub-band encoding system - Google Patents

Abstract

PURPOSE:To evade overflow in the midst of an arithmetic operation and to minimize regenerated error dispersion with simple constitution by updating the reference value of the absolute value added sum of impulse responses so as to be within an allowable value and correcting and establishing a filter coefficient. CONSTITUTION:In the case of developing the tandem connection of filter banks to parallel constitution, the sub band filter banks h0-h1 of two-band division to be bases and a tandem connection step number M are decided and a normalization processing is performed so as to let the impulse response of the filter bank satisfy SIGMAh0<2>(n)=SIGMAh1<2>(n)=1/BETA. Then, the tandem connection of the filter banks is developed to the parallel constitution, the impulse response for realizing respective frequency bands by one filter circuit is obtained and the absolute value sum is calculated. The impulse response is established when the value is below the prescribed normal value of a dynamic range to the entire frequency bands, the value of beta is updated when the band above the normal value is present and a series of operations is repeated until it becomes below the normal value. Thus, the overflow in the midst of the arithmetic operation is evaded.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a subband coding apparatus for images, audio signals, etc. by fixed point arithmetic.

[0002]

2. Description of the Related Art As one method for band-division encoding a digital signal, a sub-band filter bank that divides an input signal into two bands is used as a basic structure, and a plurality of filter banks are connected in cascade to form a band. A method of dividing is known.

The basic structure of this subband filter bank is generally as shown in FIG.

Reference numeral 1 denotes a digital filter circuit which outputs a low frequency component of the input digital signal x (n), and 2 denotes a digital filter circuit which outputs a high frequency component of the input digital signal x (n). Is a sampling circuit that down-samples the output of the filter circuit at a sampling ratio of 2: 1. The down-sampled signal is quantized and encoded. In order to reconstruct the original signal, first, 0 interpolation is performed in 4 at a sampling ratio of 1: 2. Reference numeral 5 is a digital filter circuit that outputs the low-frequency component of the output of the interpolator, and 6 is a digital filter circuit that outputs the high-frequency component of the output of the interpolator. Reproduce.

FIG. 3 shows an example of attempting frequency division into two or more bands using the subband filter bank. Here, sub-band filter banks are connected in multiple stages only for the output of the low-pass filter to realize band division, and a total of four band divisions are performed.

Further, FIG. 4 shows an example of attempting frequency division of two or more bands into a two-dimensional input signal using the subband filter bank. Here, a set of a filter circuit 8 for frequency division in the horizontal direction and a filter circuit 9 for frequency division in the vertical direction is connected in three stages to divide a total of 10 bands. FIG. 5 shows how the band is divided.

In FIG. 2, filter circuits 1, 2, 5,
If the relational expression called the perfect reconstruction condition is satisfied between the impulse responses of 6, the output signal

[0008]

[Equation 1]

Can be matched exactly with the input signal X (n). As a method of constructing a filter bank for realizing such band division, M. Smith and
T. P. "Exac by Barnwell III
t reconstruction technique
es for tree-structured su
bbband coders '' (IEEE Tran
s. on Acoustic. , Speech, Sig
nal Processing, pp. 434-44
1, June. 1986. ), And I. Daubechi
es by “Orthogonal bases of
compactly supported wave
Lets '' (Comm. Pure Appl. Ma
th. , Pp. 909-996, Nov. 1988. )
Have been reported.

However, when the above filter bank is realized by fixed-point arithmetic, even if the filter bank itself does not cause an overflow, the cascade connection may cause an overflow.

When quantizing the output of the filter bank, the conditional expression imposed on the quantizer in each frequency band in order to minimize the reproduction error variance at a given transmission rate is J. Katto and Y. Yas
"Performance evaluation by uda
ation of subband coding
d optimization of it's fill
ter coefficiencies '' (Proc.o
f Visual Commun. andImage
Processing '91, pp. 95-106,
Nov. 1991).

However, although this document shows a relational expression that should be established between the reproduction error variance and the quantization error variance of each frequency band, the concrete quantization of each frequency band as a fixed-point arithmetic operation. It does not mention how to design the vessel. When the quantizer is designed based on this conditional expression, it is generally necessary to prepare a different quantizer for each frequency band.

[0013]

That is, an object of the present invention is to realize a band division circuit based on cascade connection of filter banks which does not cause overflow during calculation, and to reproduce a reproduction error under a given transmission rate. It is to provide an approximate design method of a quantizer that minimizes, and a quantizer with a simple configuration.

[0014]

In order to solve the above-mentioned problems, the present invention has a sub-band filter bank as a basic structure which divides an input digital signal into two bands, and the filter banks are arranged in a plurality of columns. In a sub-band coding device that performs band division by connecting and quantizes signals in each frequency band, each frequency band is obtained by a single-stage filtering process when the cascade connection configuration of filter banks is expanded to a parallel configuration. Means for calculating the absolute value addition sum of the impulse response for, and if the value is larger than a predetermined allowable value, the predetermined reference value is updated and the filter coefficient of the filter bank is set to this reference value. The first feature is that the correction is made, and if it is smaller than the allowable value, the filter coefficient of the filter bank is determined.

A second feature of the present invention is that, when performing the quantization, the quantization step size of each frequency band is determined according to a proportional equation determined from the value of the reference value.

Further, according to the present invention, when the reference value is updated, the reference value is multiplied by 4 when the input digital signal is one-dimensional, and the reference value is doubled when the input digital signal is two-dimensional. The third feature is that the reference value is updated by.

[0017]

The operation of the present invention is as follows.

In FIG. 2, after the input signal x (n) passes through the filter circuit 1 or the filter circuit 2, its dynamic range is

[0019]

[Equation 2]

It is doubled (p = 0,1). further,
When the filter banks are cascade-connected as shown in FIG. 3, the dynamic range is calculated when the number of cascade connections is M and the impulse response of the filter equivalent to M-stage connection is h ′ _M (n).

[Equation 3]

[0021]

Doubled. This h ' _M (n) recursively

[0023]

[Equation 4]

Is given by

FIG. 1 shows a filter coefficient changing process for realizing a sub-band filter bank by fixed point arithmetic with a finite bit length. First, in step 10, the basic two-band split sub-band filter bank and the number of cascade connection stages M are determined. Next, at 11, the impulse response of the filter bank is

[0026]

[Equation 5]

Normalization processing is performed so as to satisfy the condition. At this time, the initial value of β is set to 1, for example. Next, in 12, according to the equation (3), the cascade connection of the filter banks is developed in a parallel configuration, and the impulse response h _M '(n) for realizing each frequency band by the one-stage filter circuit is obtained, and its absolute value is obtained. sum

[0028]

[Equation 6]

Calculate

Next, at 13, if the value of the above equation for all frequency bands is less than or equal to the specified value DR given in advance to define the dynamic range, the processing is ended thereby, and at 16 Determine the impulse response of the filter bank. On the other hand, when there is a band in which the sum of absolute difference is equal to or more than DR, the value of β is updated in 14 and the impulse response is updated in accordance with the equation (4) in 15 and returns to 12 again to satisfy the above condition. Repeat a series of operations until. As long as the impulse response given in this way is used, overflow during the calculation can be completely avoided.

Next, optimization of quantization will be described. If the filter coefficients are orthogonal, the impulse response of the synthesis filter bank is

[0032]

[Equation 7]

Satisfies the condition

When a quantization operation is applied to a band division system in which the filter banks are connected in cascade, and this is used as subband coding, the optimum quantization in FIG. Katto and Y. “Performance evaluation o” by Yasuda
f subband coding and opti
migration of it's filter co
Efficients '' (Proc. of Visu
al Commun. and Image Proce
ssing '91, pp. 95-106, Nov. 1
According to 991),

[0035]

[Equation 8]

Is satisfied. At this time,

[0037]

[Equation 9]

Is a band band (= Low, Middl
e, High) quantization error variance,

[0039]

[Equation 10]

Is the reproduction error variance of the decoded signal. Therefore, the quantization step size for each frequency band

[0041]

[Equation 11]

By the above, optimum quantization can be realized approximately. Therefore, in FIG. 1, when the updating process ends in 13, the quantization step width of each frequency band is determined according to the equation (8) using the value of β that gives the final impulse response of the filter bank.

When β ≠ 1, it is generally necessary to prepare different quantizers for each frequency band. However,
If the specified value β is set to a multiple of 4, this results in a shift operation before quantization for each band. Therefore, only one quantizer needs to be prepared.

This corresponds to starting the update process with the initial value of β at 1 in FIG. 1 and multiplying the value of β by 14 at 14.

[0045] In the case of two dimensions, it can be decomposed impulse response _{h 'M (m, n)} = h' M (m) · h 'M (n) and (9). Therefore, in the cascade connection of M horizontal stages and vertical M stages shown in FIG. 4, the dynamic range is

[0046]

[Equation 12]

Doubled. Therefore, in 12 of FIG.
By replacing the absolute value addition and sum portion shown in the equation (5) with the equation (10), the impulse response can be updated as in the one-dimensional case.

Next, when a quantization operation is applied to a two-dimensional band division system in which filter banks are connected in cascade, and this is used as sub-band coding, taking the case of FIG. 4 as an example, optimum quantization is performed. Is

[0049]

[Equation 13]

Is defined as satisfying Therefore, the quantization step size for each frequency band

[0051]

[Equation 14]

By the above, optimum quantization can be realized approximately. Therefore, in FIG. 1, when the updating process ends in 13, the quantization step width of each frequency band is determined according to the equation (12) using the value of β that gives the final impulse response of the filter bank.

When β ≠ 1, it is generally necessary to prepare different quantizers for each frequency band. However, if the specified value β is set to a multiple of 2, this results in a shift operation before quantization for each band. Therefore, only one quantizer needs to be prepared. This corresponds to starting the updating process with the initial value of β at 1 in FIG. 1 and doubling the value of β at 14.

[0054]

EXAMPLES Next, examples of the present invention will be described. Tables 1 and 2 are obtained as the first embodiment of the present invention to obtain the expansion of the dynamic range for each band in the case of β = 1 and the case of β = 2 in FIG. Here, L is the filter length, and H.
Caglar, Y .; Liu and A. N. Akan
su "Statistically Optimize
d PR-QMF Design '' (SPIE VS
IP'91, pp. 86-94, Nov. 199
1. ) Is used.

[0055]

[Table 1]

From Table 1, it can be seen that when β = 1, the dynamic range is expanded from 11 times (L = 4) to 18 times (L = 8) in the lowest frequency region. Therefore, when this is realized by fixed-point arithmetic, the spread of the dynamic range is 4 to 5 bits. On the other hand, in the case of β = 2, as can be seen from Table 2, the dynamic range is only expanded at most about twice. Therefore, when this is realized as a fixed-point arithmetic, the spread of the dynamic range is 1 to 2 bits.

[0057]

[Table 2]

Next, FIGS. 6 and 7 show a moving picture coding apparatus as a second embodiment of the present invention. Assuming that the filter length is 4 and the input image is represented by 8 bits, the bit representation when β = 1 is as shown in FIG. 6, and the bit representation when β = 2 is as shown in FIG. 7.

Here, a lightly shaded portion shows an effective bit length, and a thickly shaded portion shows a quantization error. From now on, β =
It can be seen that by setting β = 2 to the case of 1, fixed-point arithmetic can be realized by 3 bits less.

[0060]

As described above, the sub-band coding apparatus according to the present invention can realize a sub-band filter bank by fixed-point arithmetic in a limited bit length range without causing overflow, and it can be approximated. Optimal quantization can be realized by shift calculation for each band and one quantizer.

[Brief description of drawings]

FIG. 1 is a method for determining a filter coefficient according to the present invention.

FIG. 2 is a 2-band division filter bank

[Fig. 3] Cascade connection of filter banks (one-dimensional)

FIG. 4 Cascade connection of filter banks (two-dimensional)

FIG. 5: Band division pattern (two-dimensional)

FIG. 6 Realization of moving image coding (β = 1)

FIG. 7: Realization of moving image coding (β = 2)

[Explanation of symbols]

 1 low-pass filter circuit 2 high-pass filter circuit 3 sub-sampling circuit 4 0 value interpolation circuit 5 low-pass filter circuit 6 high-pass filter circuit 7 adder circuit 8 horizontal direction filter circuit 9 vertical direction filter circuit 10 determination of basic configuration 11 β initialization, impulse response Normalization 12 Calculation of sum of absolute values of impulse response in parallel expression 13 Conditional branch based on sum of absolute values 14 Update value of β 15 Update impulse response according to value of β 16 Determine impulse response and quantization step size

Claims (3)

[Claims] 1. A sub-band filter bank that divides an input digital signal into two bands is used as a basic structure, and band division is performed by connecting a plurality of the filter banks in cascade to quantize a signal in each frequency band. In the subband coding device, a means for calculating an absolute value sum of impulse responses for obtaining each frequency band by a one-step filtering process when the cascade connection configuration of filter banks is developed, and its value are If it is larger than a predetermined allowable value, a predetermined reference value is updated and the filter coefficient of the filter bank is modified with this reference value. If it is smaller than the allowable value, the filter coefficient of the filter bank is determined. A subband coding apparatus comprising: 2. The subband coding apparatus according to claim 1, wherein, when performing the quantization, a quantization step size of each frequency band is determined according to a proportional expression determined from the reference value. 3. When updating the reference value, the reference value is multiplied by four when the input digital signal is one-dimensional and doubled when the input digital signal is two-dimensional. The subband coding apparatus according to claim 1, wherein the value is updated.