CN100456636C - Two kinds of network structure of full-phase DCT/IDCT digital filter - Google Patents

Abstract

The present invention provides two network structures of a full-phase DCT/IDCT digital filter, which comprises a time domain network structure and a prevalence-rate domain network structure, wherein the time domain network structure comprises GN conversion; the prevalence-rate domain network structure comprises GN< T > conversion; all delay units are orderly connected with each other in series, and the number of the delay units is 2 (N-1); the first delay unit is a signal input end; in the two network structures, for a point x (n) in a time sequence, the definition of the data points of which the number is 2N-1 is expressed as following: [x (n+N-1), x (n+N-1), x (n+N-2),..., x (n),..., x (n-N+3), x (n-N+2), x (n-N+1)], and the data points are obtained by z (0) =x (n); z (1) =x (n+1) +x (n-1); z (2) =x (n+2) +x (n-2);......, z (n-1) =x (n+N-1) +x (n-N+1); the output of a filter of the time domain network structure is obtained by the result of prevalence-rate response F< N > converted by GN doing inner product with a Z vector; the output of a filter of the prevalence-rate domain network structure is obtained by prevalence-rate response FN doing the inner product with the result of a Z vector converted by GN< T >. The present invention converts DCT/IDCT conversion for twice into GN or GN< T > conversion for one time and has the advantages that the complexity of filtering calculation is simplified by simplifying the filter structure; the dominance of IDCT/DCT in filtering can be better exerted.

Description

Two kinds of network configurations of full-phase DCT/IDCT digital filter

Technical field

The invention belongs to a kind of filter that is used for signal processing, be specifically related to the network implementation structure of digital filter.

Technical background

DCT (discrete cosine transform) calculates with DFT (discrete Fourier transform (DFT)) and does not comparatively speaking need complex operation, in order to give full play to the application potential of DCT in digital filtering, full phase place thought and DCT combined to design the good FIR filter of amplitude-frequency characteristic with linear phase.The implementation structure of full-phase DCT/IDCT (inverse discrete cosine transform) digital filter is the implementation structure that adopts direct row rate territory at present.But this implementation structure is comparatively complicated, need carry out twice the positive inverse transformation of DCT/IDCT, as shown in Figure 1.Discrete cosine transform and inverse discrete cosine transform are as discrete Fourier transform (DFT), and calculation of complex will expend the long period.For the ease of realizing full-phase DCT/IDCT digital filter with hardware-efficient ground.If adopt the network configuration of full-phase DCT/IDCT digital filter, the implementation structure twice DCT/IDCT in the row rate territory become G one time _NOr G _N ^TConversion (G _NAnd G _N ^TBeing defined in hereinafter of conversion provides), then can greatly simplify the complexity that filtering is calculated.

Summary of the invention

The purpose of this invention is to provide two kinds of network configurations being convenient to realize full-phase DCT/IDCT digital filter with hardware-efficient ground.

Illustrated below in conjunction with accompanying drawing 2 and 3 pairs of technical schemes of the present invention of accompanying drawing: two kinds of network configurations of full-phase DCT/IDCT digital filter are divided into time domain network structure and row rate territory network configuration.Two kinds of network configurations all comprise multiplier, adder and delay cell.What its two kinds of network configurations of full-phase DCT/IDCT digital filter were different is: time domain network structure comprises G _NConversion, and row rate territory network configuration comprises G _N ^TConversion, the calculating of two kinds of networks is also different simultaneously.

No matter time domain network structure or row rate territory network configuration, the individual delay cell of all 2 (N-1) is connected in series successively, and first delay cell is signal input part.For 1 x (n) in the time series, define 2N-1 data point and be expressed as: [x (n+N-1), x (n+N-2), x (n+N-3),, x (n) ... x (n-N+3), x (n-N+2), x (n-N+1)], because full-phase DCT/IDCT digital filter is a kind of digital filter of zero phase, and the length of filter is odd number 2N-1, thereby Filter Structures can be expressed as the form of first kind linear phase network configuration.Fig. 2 is exactly the formal argument by first kind linear phase network configuration.The Z vector is a column vector, by z (0)=x (n);

z(1)＝x(n+1)+x(n-1)；z(2)＝x(n+2)+x(n-2)；......，

Z (N-1)=x (n+N-1)+x (n-N+1) obtains.

The output of time domain network structure filter is by row rate response F _NThrough G _NResult after the conversion and Z vector are done inner product and are obtained.

And respond F by the row rate for the output of row rate territory network configuration filter _NWith the Z vector through G _N ^TResult after the conversion does inner product and obtains.

The point of the need filtering in x (n) the express time sequence wherein, the point in all the other time serieses is the time delay of being done with respect to x (n); 2N-1 represents total the counting of data in the used time series; The value of each component marks in Fig. 2 and Fig. 3 in the Z vector sum vector.

Description of drawings

Accompanying drawing 1 is the direct implementation structure in DCT/IDCT digital filter row rate territory of twice in full phase place.

Accompanying drawing 2 is the time domain network structure of full-phase DCT/IDCT digital filter.F among the figure _NBe the response of row rate.

Accompanying drawing 3 is the row rate territory network configuration of full-phase DCT/IDCT digital filter.

Embodiment

Below the present invention is further illustrated by the following examples.

For the IDCT-inverse discrete cosine transform,

$G_N(m,n)=\left\{\begin{array}{cc}\frac{1}{N}& m=\mathrm{0,0}\&le;n\&le;N-1\\ \frac{N-m+\sqrt{2}-1}{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="C20061001357700081.png,C20061001357700091.png"\; state="\{\{state\}\}">N</figure-callout>}}^2}\cos \frac{(2n+1)\mathrm{m\&pi;}}{2\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="C20061001357700082.png,C20061001357700091.png"\; state="\{\{state\}\}">N</figure-callout>}}& 0\&le;n\&le;N-\mathrm{1,1}\&le;m\&le;N-1\end{array}\right.---\left(1\right)$

$G_N^T(m,n)=\left\{\begin{array}{cc}\frac{1}{N}& n=\mathrm{0,0}\&le;m\&le;N-1\\ \frac{N-m+\sqrt{2}-1}{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="C20061001357700081.png,C20061001357700091.png"\; state="\{\{state\}\}">N</figure-callout>}}^2}\cos \frac{(2n+1)\mathrm{m\&pi;}}{2\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="C20061001357700082.png,C20061001357700091.png"\; state="\{\{state\}\}">N</figure-callout>}}& 0\&le;m\&le;N-\mathrm{1,1}\&le;n\&le;N-1\end{array}\right.---\left(2\right)$

Formula (1) is at inverse discrete cosine transform, matrix G _NExpression formula (Fig. 2); Formula (2) is at inverse discrete cosine transform, matrix G _N ^TExpression formula (Fig. 3).Wherein 2N-1 represents the length of filter; M represents row; N represents row.

In like manner for the DCT-discrete cosine transform,

The following examples are example with IDCT.Be G _NAnd G _N ^TBe taken as (1), (2) formula respectively.

In the time domain implementation structure, present embodiment delay cell is 6, promptly chooses N=4, and then the length of full-phase DCT/IDCT digital filter is 7.For 1 x (n) in the time series, define 2N-1 data point and be expressed as: [x (n+3), x (n+2), x (n+1), x (n), x (n-1), x (n-2), x (n-3)], x (n+3) becomes x (n-3) after 6 delay cell.Then the Z vector is z (0)=x (n), z (1)=x (n+1)+x (n-1), z (2)=x (n+2)+x (n-2), z (3)=x (n+3)+x (n-3).The output of filter is by row rate response F _NThrough G _NResult after the conversion and Z vector are done inner product and are obtained.Promptly

$G_4(m,n)=\left\{\begin{array}{cc}\frac{1}{N}& m=\mathrm{0,0}\&le;n\&le;3\\ \frac{N-m+\sqrt{2}-1}{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="C20061001357700081.png,C20061001357700091.png"\; state="\{\{state\}\}">N</figure-callout>}}^2}\cos \frac{(2n+1)\mathrm{m\&pi;}}{2\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="C20061001357700082.png,C20061001357700091.png"\; state="\{\{state\}\}">N</figure-callout>}}& 0\&le;n\&le;3,1\&le;m\&le;3\end{array}\right.$

F ₄＝[F(0)，F(1)，F(2)，F(3)]

Make h ₄=G ₄F ₄

Then the filtering corresponding to 1 x (n) in the time series is output as:

y(n)＝(Z，h ₄)＝z(0)*h(0)+z(1)*h(1)+z(2)*h(2)+z(3)*h(3)。Multiplication during inner product is calculated and the addition multiplier among network configuration Fig. 2

And adder

Obtain.

In the implementation structure of row rate territory, the number of present embodiment delay cell is taken as 6, promptly chooses N=4, and then the length of full Phase DFT Digital Filter Using is 7.For 1 x (n) in the time series, define 2N-1 data point and be expressed as: [x (n+3), x (n+2), x (n+1), x (n), x (n-1), x (n-2), x (n-3)], x (n+3) becomes x (n-3) after 6 delay cell.Then the Z vector is z (0)=x (n), z (1)=x (n+1)+x (n-1), z (2)=x (n+2)+x (n-2), z (3)=x (n+3)+x (n-3).Then the output of filter is by row rate response F _NWith the Z vector through G _N ^TResult after the conversion does inner product and obtains.

That is:

$G_4^T(m,n)=\left\{\begin{array}{cc}\frac{1}{N}& n=\mathrm{0,0}\&le;m\&le;3\\ \frac{N-m+\sqrt{2}-1}{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="C20061001357700081.png,C20061001357700091.png"\; state="\{\{state\}\}">N</figure-callout>}}^2}\cos \frac{(2n+1)\mathrm{m\&pi;}}{2\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="C20061001357700082.png,C20061001357700091.png"\; state="\{\{state\}\}">N</figure-callout>}}& 0\&le;m\&le;3,1\&le;n\&le;3\end{array}\right.,$ Again

F ₄=[F (0), F (1), F (2), F (3)], order

$V_4=G_4^T\&CenterDot;Z_4$

Filtering corresponding to 1 x (n) in the time series is output as:

y(n)＝(V ₄，F ₄)＝V(0)*F(0)+V(1)*F(1)+V(2)*F(2)+V(3)*F(3)。Multiplication and addition during inner product is calculated obtain with multiplier among network configuration Fig. 3 and adder.

Characteristics of the present invention are: twice conversion in the direct implementation structure in row rate territory (the positive inverse transformation of DCT/IDCT) become G one time_NOr G_N ^TConversion. Here mainly be the number of times that has reduced the DCT/IDCT conversion, and DCT/IDCT Conversion will expend the long period. So, simplified the complexity that filtering is calculated by simplifying filter construction. Exist simultaneously The IDCT/DCT territory does not need plural number to calculate than the DFT territory, and implementation structure can be brought into play after computation complexity is reduced better The advantage of IDCT/DCT in filtering.

Claims (2)

1. the time domain network structure of full-phase DCT/IDCT digital filter comprises multiplier, adder, G _NConversion and delay cell, the individual delay cell of all 2 (N-1) is connected in series successively, N is a positive integer, first delay cell is signal input part, the time domain network structure that it is characterized in that full-phase DCT/IDCT digital filter defines 2N-1 data point and is expressed as for 1 x (n) in the time series:

[x (n+N-1), x (n+N-2), x (n+N-3) ..., x (n) ..., x (n-N+3), x (n-N+2), x (n-N+1)], column vector is the Z vector, by z (0)=x (n); Z (1)=x (n+1)+x (n-1); Z (2)=x (n+2)+x (n-2); ..., z (N-1)=x (n+N-1)+x (n-N+1) obtains, and wherein the n value is an integer, and span is-∞＜n＜∞ that the output of filter is by row rate response F _NThrough G _NResult after the conversion and Z vector are done inner product and are obtained, and wherein need the point of filtering in x (n) the express time sequence, and the point in all the other time serieses is the time delay of being done with respect to x (n); 2N-1 represents total the counting of data in the used time series, G _NTransform definition is

h _N＝G _NF _N

For the IDCT-inverse discrete cosine transform,

$G_N(m,n)=\left\{\begin{array}{cc}\frac{1}{N},& m=\mathrm{0,0}\&le;n\&le;N-1,\\ \frac{N-m+\sqrt{2}-1}{N^2}\cos \frac{(2n+1)\mathrm{m\&pi;}}{2N},& 0\&le;n\&le;N-\mathrm{1,1}\&le;m\&le;N-1.\end{array}\right.$

For the DCT-discrete cosine transform,

$G_N(m,n)=\left\{\begin{array}{cc}\frac{N-m}{N^2},& n=\mathrm{0,0}\&le;m\&le;N-1,\\ \frac{1}{N^2}[(N-m)\cos \frac{\mathrm{mn\&pi;}}{N}-\csc \frac{\mathrm{n\&pi;}}{N}\sin \frac{\mathrm{mn\&pi;}}{N}],& 1\&le;n\&le;N-1,0\&le;m\&le;N-1.\end{array}\right.$

Wherein, m represents row, and n represents row.

2. the row rate territory network configuration of full-phase DCT/IDCT digital filter comprises multiplier, adder, G _N ^TConversion and delay cell, delay cell 2 (N-1) is individual is connected in series successively for all, N is a positive integer, first delay cell is signal input part, the row rate territory network configuration that it is characterized in that full-phase DCT/IDCT digital filter defines 2N-1 data point and is expressed as for 1 x (n) in the time series:

[x (n+N-1), x (n+N-2), x (n+N-3) ..., x (n) ..., x (n-N+3), x (n-N+2), x (n-N+1)], column vector is the Z vector, by z (0)=x (n); Z (1)=x (n+1)+x (n-1); Z (2)=x (n+2)+x (n-2); ..., z (N-1)=x (n+N-1)+x (n-N+1) obtains, and wherein the n value is an integer, and span is-∞＜n＜∞ that the output of filter is by row rate response F _NWith the Z vector through G _N ^TResult after the conversion does inner product and obtains, the point of the need filtering in x (n) the express time sequence wherein, and the point in all the other time serieses is to do time delay with respect to x (n); 2N-1 represents total the counting of data in the used time series, G _N ^TTransform definition is

$V_N=G_N^{T}Z$

For the IDCT-inverse discrete cosine transform,

$G_N^T(m,n)=\left\{\begin{array}{cc}\frac{1}{N},& n=\mathrm{0,0}\&le;m\&le;N-1,\\ \frac{N-n+\sqrt{2}-1}{N^2}\cos \frac{(2m+1)\mathrm{n\&pi;}}{2N},& 0\&le;m\&le;N-\mathrm{1,1}\&le;n\&le;N-1.\end{array}\right.$

For the DCT-discrete cosine transform, for

$G_N^T(m,n)=\left\{\begin{array}{cc}\frac{N-n}{N^2},& m=\mathrm{0,0}\&le;n\&le;N-1,\\ \frac{1}{N^2}[(N-n)\cos \frac{\mathrm{mn\&pi;}}{N}-\csc \frac{\mathrm{m\&pi;}}{N}\sin \frac{\mathrm{mn\&pi;}}{N}],& 1\&le;m\&le;N-1,0\&le;n\&le;N-1.\end{array}\right.$

Wherein, m represents row, and n represents row.

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