CN101763629B - Construction method of integrative filter bank with cellular structure - Google Patents

Abstract

The invention relates to a construction method of an integrative filter bank with a cellular structure. The invention has the following technical scheme: firstly, sub-band noise is modeled, and a sub-band noise model is described into a linear time invariant system; when an input signal of a system is white noise, the spectrum of an output signal is the same as the spectrum of the sub-band noise n(k), and the function of the system is marked as Wn(z); and then, a multiphase component R(z) of the optimal integrative filter bank with the cellular structure is determined according to the cellular structure of a multiphase component E(z) of an analytic filter bank, then an original image x(n) is reconstructed by utilizing the integrative filters corresponding to the multiphase component R(z) to obtain a reconstructed image, and the reconstructed image meets the minimum power spectrum norm of an error signal e(n). The invention takes the minimum power spectrum norm of the reconstructed error signal e(n) as a design basis and constructs the multiphase component R(z) of the integrative filter bank with a linear phase and the cellular structure, so that the peak signal-to-noise ratio of the reconstructed image is maximum, and the sub-band denoising effect of the image is optimal.

Description

A kind of building method of lattice structure synthesis filter group

Technical field

The invention belongs to image subband noise-removed technology field.Be specifically related to a kind of building method of lattice structure synthesis filter group.

Background technology

The complete reconfigurable filter group of linear phase is widely used in the Flame Image Process, and a lot of people are devoted to study theory, design and the application of the complete reconfigurable filter group of linear phase.The complete reconfigurable filter group of linear phase can realize with lattice structure, has so both kept the character of complete reconstruct, and can have been realized fast.Lattice structure is used for the complete reconfigurable filter group of linear phase of two passages the earliest, is used for the imitative complete reconfigurable filter group of linear phase at the tenth of the twelve Earthly Branches of M passage afterwards, and is generalized in the linear-phase filter group with imitative unitarity matter.The over-sampling bank of filters has more superiority than threshold sampling bank of filters, as the degree of freedom of design, the raising of denoising performance and good robust performance etc.Gan and Ma have some researchs (L.Gan and K.-K.Ma to the lattice structure and the application thereof of the complete reconstruct over-sampling of linear phase bank of filters, " Oversampled linear-phase perfectreconstruction filterbanks:theory; lattice structure and parameterization; " IEEE Trans.SignalProcessing, vol.51, no.3, pp.744-759, Mar.2003).

Be used for denoising the synthesis filter group method for designing the someone study (H.Vikalo, B.Hassibi, A.T.Erdogan, and T.Kailath, " On robust signal reconstruction in noisy filter banks; " Signal Processing, vol.85, pp.1-14,2005), but this method has only been considered the situation of threshold sampling, and designed synthesis filter group does not have complete reconstruction nature.Verified (the H.B ¨ olcskei of Frame Theory method, F.Hlawatsch, and H.G.Feichtinger, " Frame-theoretic analysis of oversampled filter banks; " IEEE Trans.Signal Processing, vol.46, pp.3256-3268, December 1998), the over-sampling analysis filter is at l ₂On have stable contraryly, and be the antithesis framework of analysis filterbank by the synthesis filter group that its complete reconstruct forms.In these antithesis frameworks, the standard antithesis framework that is obtained by the generalized inverse of analysis filterbank has two minimum norms, and the known noise of power spectrum density is had optimum subband denoising performance.Be used for denoising the over-sampling bank of filters building method also the someone study.But the existing over-sampling filter set designing method that is used for denoising can not guarantee that bank of filters has lattice structure, thereby they can not be used for designing the lattice structure over-sampling bank of filters with linear phase.The synthesis filter group of this method design has the characteristics of complete reconstruct, linear phase and lattice structure, and in satisfying the synthesis filter group of these conditions, the power spectrum norm minimum of the error signal that image is reconstructed.

Summary of the invention

The present invention is intended to overcome the prior art defective, and purpose provides a kind of Y-PSNR maximum of reconstructed image, the building method of the lattice structure synthesis filter group that denoising performance is good.

For finishing above-mentioned task, the technical solution used in the present invention is: the mark that will relate to this programme earlier is unitedly described as follows:

P is an even number, expression channel transmitted number; n _sExpression balanced-filter number; n _aThe title number of filter that makes difficulties, n _a=n _s=P/2; M represents to extract number, and M=2m, m are natural number; L represents the length of analysis filterbank; Subscript-1 representing matrix contrary; The transposition of subscript T representing matrix; I _nExpression n rank unit matrix; J _nThe counter-rotating matrix of expression n rank unit matrix; Diag () represents diagonal matrix; z ^-1Represent a unit time-delay; W _2nThe expression butterfly structure,

Analysis filterbank and synthesis filter group all are linear phases.

The process of lattice structure synthesis filter set constructor method is: at first to the subband noise modeling, the subband noise model is described as a linear time invariant system, when the input signal of system was white noise, the spectrum of output signal was identical with the spectrum of subband noise n (k), and system function is designated as W _n(z); Determine a kind of heterogeneous components R (z) of lattice structure synthesis filter group of optimum again according to the lattice structure of the heterogeneous component E (z) of analysis filterbank, utilize the corresponding synthesis filter of heterogeneous components R (z) that original image x (n) is reconstructed then, obtain reconstructed image

Reconstructed image

Satisfy the power spectrum norm minimum of error signal e (n).The heterogeneous component E (z) of the lattice structure analysis filterbank with linear phase of known transmitting terminal,

E(z)＝G _k(z)G _k-1(z)…G ₁(z)E ₀(z )(1)

In the formula (1):

$K=\frac{L}{M}-1$

In the formula (2):

i＝1，2，…，k；

U _iBe n _s* n _aInvertible matrix;

n＝P/2＝n _s＝n _a；

In the formula (3):

U ₀Be n _s* [M/2] but the left inverse matrix;

V ₀Be n _a* [M/2] but the left inverse matrix;

The system function of known subband noise model is W _n(z), then the heterogeneous components R (z) of Zui You lattice structure synthesis filter group is,

R(z)＝R _0opt(z)z ^-1G ₁ ^-1(z)…z ^-1G _k-1 ^-1(z)z ^-1G _k ^-1(z) (4)

In the formula (5):

X _1optBe [M/2] * n _sMatrix,

X _2optBe [M/2] * n _aMatrix,

In formula (7), (8):

Ψ ₁₁Be n _s* n _sInvertible matrix;

Ψ ₂₂Be n _a* n _aInvertible matrix;

U ₀Be n _s* [M/2] but the left inverse matrix;

V ₀Be n _a* [M/2] but the left inverse matrix.

The power spectrum norm of described error signal e (n) is:

‖e‖ ₂＝‖R(z)W(z)‖ ₂ (9)

Described Ψ ₁₁And Ψ ₂₂Be the block diagonal matrix of Ψ, wherein:

Ψ or try to achieve by following formula:

In the formula (10):

Φ is Lyapunov equation Φ-A Φ A ^T=BB ^TSeparate; A, B, C, D are the state space variable of the corresponding system of transport function W (z);

W _n(z) be the system function of subband noise model;

W(z)＝D+C×(zI-A) ^-1×B；

Ψ or try to achieve by following formula:

$\mathrm{\Ψ}=\underset{i=0}{\overset{N}{\mathrm{\Σ}}}{W}_i{W}_i^T---\left(11\right)$

In the formula (11):

The lattice structure performing step of the heterogeneous component E (z) of described analysis filterbank is as follows:

(1) M group input signal is numbered 0 to M-1;

(2) M group input signal carries out butterfly computation;

(3) output signal that is obtained by step (2) multiply by coefficient 2 ^-1/2

(4) in the output signal that is obtained by step (3), be divided into two parts up and down in order, every part has m group signal, and the first half m group signal is through module U ₀, obtain n _sThe group output signal;

(5) in the output signal that is obtained by step (3), the latter half m group signal is through module V ₀, obtain n _aThe group output signal;

(6) n that obtains by step (4) _sGroup output signal and the n that obtains by step (5) _aGroup output signal P group output signal is altogether carried out butterfly computation, and the output signal behind the butterfly computation is divided into two parts up and down in order, and the first half has n _sThe group output signal, the latter half has n _aThe group output signal;

(7) in the output signal that obtains by step (6), the latter half n _aZ of unit of group output signal time-delay ^-1

(8) the first half n that obtains by step (6) _sGroup output signal and the n that obtains by step (7) _aGroup output signal P group output signal is altogether carried out butterfly computation;

(9) in the output signal that obtains by step (8), the first half n _sThe group signal is through module U ₁

(10) all P group output signals multiply by coefficient 1/2;

(11) step (6) to (10) is lattice structure G ₁(z) specific implementation step;

(12) through G ₁(z) signal will pass through G ₂(z) to G _k(z), G ₂(z) to G _k(z) and G ₁(z) structure is identical, just module U _iIn the parameter difference, i=1 wherein, 2 ..., k.

The lattice structure performing step of the heterogeneous components R (z) of described synthesis filter group is as follows:

(1) P group input signal is numbered 0 to P-1, passes through module z successively ^-1G _k ^-1(z) to z ^-1G ₂ ^-1(z);

(2) through module z ^-1G ₂ ^-1(z) output signal multiply by coefficient 1/2, and output signal is divided into two parts up and down in order, and the first half has n _sThe group output signal, the latter half has n _aThe group output signal;

(3) the first half n that obtains by step (2) _sThe group output signal is through module U ₁ ^-1

(4) the latter half n that obtains by step (2) _aGroup output signal and the n that obtains by step (3) _sGroup output signal P group output signal is altogether carried out butterfly computation, and the output signal behind the butterfly computation is divided into two parts up and down in order, and the first half has n _sThe group output signal, the latter half has n _aThe group output signal;

(5) the first half n that obtains by step (4) _sZ of unit of group output signal time-delay ^-1

(6) the latter half n that obtains by step (4) _aGroup output signal and the n that obtains by step (5) _sGroup output signal P group output signal is altogether carried out butterfly computation, and the output signal behind the butterfly computation is divided into two parts up and down in order, and the first half has n _sThe group output signal, the latter half has n _aThe group output signal;

(7) step (2) is lattice structure module z to step (6) ^-1G ₁ ^-1(z) specific implementation step;

(8) through z ^-1G ₁ ^-1(z) to pass through module z successively before the signal ^-1G _k ^-1(z) to z ^-1G ₂ ^-1(z), z ^-1G _k ^-1(z) to z ^-1G ₂ ^-1(z) and z ^-1G ₁ ^-1(z) structure is identical, just module U _i ^-1In the parameter difference, i=1 wherein, 2 ..., k;

(9) P that is obtained by step (6) organizes in the output signal, the first half n _sThe group output signal is through module X _1optObtain m group output signal afterwards;

(10) P that is obtained by step (6) organizes in the output signal, the latter half n _aThe group output signal is through module X _2optObtain m group output signal afterwards;

(11) all M=2m group output signals multiply by coefficient 2 ^-1/2

(12) output signal that is obtained by step (11) is carried out butterfly computation.

Owing to adopt technique scheme, the present invention with the power spectrum norm minimum of the error signal e (n) of reconstruct as design considerations, realize the denoising of image subband with lattice structure synthesis filter group, heterogeneous components R (z) with lattice structure synthesis filter group of linear phase is to heterogeneous component E (z) reconstruct fully of lattice structure analysis filterbank with linear phase.Heterogeneous component E (z) for a given lattice structure analysis filterbank with linear phase, the heterogeneous components R (z) of the lattice structure synthesis filter group with linear phase that satisfies the complete reconstruct of over-sampling is not unique, utilize this not uniqueness, the present invention is directed to the known interchannel noise model of power spectrum density, with the power spectrum norm minimum of the error signal e (n) of reconstruct as design considerations, constructed a kind of heterogeneous components R (z) with lattice structure synthesis filter group of linear phase, because the power spectrum norm minimum of error signal e (n), so, the Y-PSNR maximum of reconstructed image makes image subband denoising effect optimum.

Description of drawings

Fig. 1 is the structured flowchart that the present invention is used for image subband denoising process;

Fig. 2 be the heterogeneous component E (z) of a kind of analysis filterbank among Fig. 1 lattice structure figure (P=4, M=2);

Fig. 3 be the heterogeneous components R (z) of a kind of synthesis filter group among Fig. 1 lattice structure figure (P=4, M=2);

Fig. 4 is subband noise n (k) generation module block diagram among Fig. 1.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is further illustrated, is not the restriction to its protection domain.

A kind of building method of lattice structure synthesis filter group.The mark that will relate to this method earlier is unitedly described as follows:

P is an even number, expression channel transmitted number; n _sExpression balanced-filter number; n _aThe title number of filter that makes difficulties, n _a=n _s=P/2; M represents to extract number, and M=2m, m are natural number; L represents the length of analysis filterbank; Subscript-1 representing matrix contrary; The transposition of subscript T representing matrix; I _nExpression n rank unit matrix; J _nThe counter-rotating matrix of expression n rank unit matrix; Diag () represents diagonal matrix; z ^-1Represent a unit time-delay; W _2nThe expression butterfly structure,

Analysis filterbank and synthesis filter group all are linear phases.

Present embodiment is used for image subband denoising process as shown in Figure 1: at first the signal x (n) with the every row of transmitting terminal image is divided into the M piece through time-delay, the signal behind the piecemeal being carried out M extracts again, obtain P group output signal after heterogeneous component E (z) conversion of signal after M extracts by the lattice structure analysis filterbank, then the P after the conversion is organized output signal by containing P the Channel Transmission of noise n (k), then obtain M and organize output signal in heterogeneous components R (z) conversion of receiving end by lattice structure synthesis filter group, at last M is organized output signal and carry out the M interpolation, the signal after the interpolation obtains reconstruction signal through the time-delay stack

The building method of the lattice structure synthesis filter group of present embodiment is: at first to the subband noise modeling, the subband noise model is described as a linear time invariant system, when the input signal of system is white noise, the spectrum of output signal is identical with the spectrum of subband noise n (k), and system function is designated as W as shown in Figure 4 _n(z); Determine a kind of heterogeneous components R (z) of lattice structure synthesis filter group of optimum again according to the lattice structure of the heterogeneous component E (z) of analysis filterbank, utilize the corresponding synthesis filter of heterogeneous components R (z) that original image x (n) is reconstructed then, obtain reconstructed image

Reconstructed image Satisfy the power spectrum norm minimum of error signal e (n).

In the present embodiment, P=4, M=2

The heterogeneous component E (z) of the lattice structure analysis filterbank with linear phase of known transmitting terminal,

E(z)＝G _k(z)G _k-1(z)…G ₁(z)E ₀(z) (1)

In the formula (1):

$K=\frac{L}{M}-1=1$

In the formula (2):

i＝1，

U ₁But be 2 * 2 inverse matrixs;

n＝2。

In the formula (3):

U ₀But be 2 * 1 left inverse matrixes;

V ₀But be 2 * 2 left inverse matrixes;

The system function of known subband noise model is W _n(z), the heterogeneous component of then optimum lattice structure synthesis filter group

R (z) is,

In the formula (5):

X _1optBe 2 * 1 matrixes,

X _2optBe 2 * 1 matrixes,

In formula (7), (8):

Ψ ₁₁Be 2 * 2 invertible matrix,

Ψ ₂₂Be 2 * 2 invertible matrix,

U ₀But be 2 * 1 left inverse matrixes;

V ₀But be 2 * 2 left inverse matrixes;

The power spectrum norm of described error signal e (n) is:

‖e‖ ₂＝‖R(z)W(z)‖ ₂ (9)

Described Ψ ₁₁And Ψ ₂₂Be the block diagonal matrix of Ψ, wherein:

Ψ or try to achieve by following formula:

In the formula (10):

Φ is Lyapunov equation Φ-A Φ A ^T=BB ^TSeparate;

$\mathrm{\Φ}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

A, B, C, D are the state space variable of the corresponding system of transport function W (z);

W _n(z) be the system function of subband noise model;

W(z)＝D+C×(zI-A) ^-1×B；

$A=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$

Ψ or try to achieve by following formula:

In the formula (11):

The lattice structure performing step of the heterogeneous component E (z) of described analysis filterbank is as shown in Figure 2:

(1) 2 group of input signal is numbered 0 to 1,

(2) 2 groups of input signals carry out butterfly computation,

(3) output signal that is obtained by step (2) multiply by coefficient 2 ^-1/2,

(4) in the output signal that is obtained by step (3), be divided into two parts up and down in order, every part has 1 group of signal, and 1 group of signal of the first half is through module U ₀, obtain 2 groups of output signals,

(5) in the output signal that is obtained by step (3), 1 group of signal of the latter half is through module V ₀, obtain 2 groups of output signals,

(6) 2 groups of output signals that obtained by step (4) and 2 groups of output signals being obtained by step (5) totally 4 groups of output signals are carried out butterfly computation, output signal behind the butterfly computation is divided into two parts up and down in order, the first half has 2 groups of output signals, and the latter half has 2 groups of output signals

(7) in the output signal that obtains by step (6), z of unit of 2 groups of output signals time-delays of the latter half ^-1,

(8) the 2 groups of output signals of the first half that obtain by step (6) and 2 groups of output signals obtaining by step (7) totally 4 groups of output signals carry out butterfly computation,

(9) in the output signal that is obtained by step (8), 2 groups of signals of the first half are through module U ₁,

(10) all 4 groups of output signals multiply by coefficient 1/2,

(11) step (6) to (10) is lattice structure G ₁(z) specific implementation step,

(12) through G ₁(z) signal will pass through G ₂(z) to G _k(z), G ₂(z) to G _k(z) and G ₁(z) structure is identical, just module U _iIn the parameter difference, i=1 wherein, 2 ..., k.

The lattice structure performing step of the heterogeneous components R (z) of described synthesis filter group is as shown in Figure 3:

(1) 4 group of input signal is numbered 0 to 3, passes through module z successively ^-1G _k ^-1(z) to z ^-1G ₂ ^-1(z),

(2) through module z ^-1G ₂ ^-1(z) output signal multiply by coefficient 1/2, and output signal is divided into two parts up and down in order, and the first half has 2 groups of output signals, and the latter half has 2 groups of output signals,

(3) 2 groups of output signals processes of the first half module U that obtains by step (2) ₁ ^-1,

(4) the 2 groups of output signals of the latter half that obtain by step (2) and 2 groups of output signals obtaining by step (3) totally 4 groups of output signals carry out butterfly computation, output signal behind the butterfly computation is divided into two parts up and down in order, the first half has 2 groups of output signals, and the latter half has 2 groups of output signals

(5) z of unit of 2 groups of output signal time-delays of the first half that obtains by step (4) ^-1,

(6) the 2 groups of output signals of the latter half that obtain by step (4) and 2 groups of output signals obtaining by step (5) totally 4 groups of output signals carry out butterfly computation, output signal behind the butterfly computation is divided into two parts up and down in order, the first half has 2 groups of output signals, and the latter half has 2 groups of output signals

(7) step (2) is lattice structure module z to step (6) ^-1G ₁ ^-1(z) specific implementation step,

(8) through z ^-1G ₁ ^-1(z) to pass through module z successively before the signal ^-1G _k ^-1(z) to z ^-1G ₂ ^-1(z), z ^-1G _k ^-1(z) to z ^-1G ₂ ^-1(z) and z ^-1G ₁ ^-1(z) structure is identical, just module U _i ^-1In the parameter difference, i=1 wherein, 2 ..., k,

(9) in 4 groups of output signals that obtained by step (6), 2 groups of output signals of the first half are through module X _1optObtain 1 group of output signal afterwards,

(10) in 4 groups of output signals that obtained by step (6), 2 groups of output signals of the latter half are through module X _2optObtain 1 group of output signal afterwards,

(11) all 2 groups of output signals multiply by coefficient 2 ^-1/2,

(12) output signal that is obtained by step (11) is carried out butterfly computation.

Present embodiment with the power spectrum norm minimum of the error signal e (n) of reconstruct as design considerations, realize the denoising of image subband with lattice structure synthesis filter group, heterogeneous components R (z) with lattice structure synthesis filter group of linear phase is to heterogeneous component E (z) reconstruct fully of lattice structure analysis filterbank with linear phase.Heterogeneous component E (z) for a given lattice structure analysis filterbank with linear phase, the heterogeneous components R (z) of the lattice structure synthesis filter group with linear phase that satisfies the complete reconstruct of over-sampling is not unique, utilize this not uniqueness, present embodiment is at the known interchannel noise model of power spectrum density, with the power spectrum norm minimum of the error signal e (n) of reconstruct as design considerations, constructed a kind of heterogeneous components R (z) with lattice structure synthesis filter group of linear phase, because the power spectrum norm minimum of error signal e (n), so, the Y-PSNR maximum of reconstructed image makes image subband denoising effect optimum.

The different noise model system function W of the known analysis filterbank of present embodiment with 6 kinds _n(z), 6 kinds of different noise model system functions are as follows respectively:

Wn5＝diag{2+0.5z ^-1，2，2，2+z ^-1}

Under 6 kinds of different noise model system function situations, adopt the present invention to construct corresponding optimal synthesis bank of filters, be that 512 * 512 Lena.bmp image is done denoising to size, the Y-PSNR that obtains is as shown in table 1.

Y-PSNR value under the different noise model system function of table 1 situation

As can be seen from Table 1, under the known situation of noise model, image is handled with the synthesis filter group of the correspondence of the present invention's structure, Y-PSNR value maximum, as seen, the synthesis filter group that the present invention constructs is optimum.

Claims (5)

1. the building method of a lattice structure synthesis filter group is characterized in that earlier mark involved in this method being unitedly described as follows:

P is an even number, expression channel transmitted number; n _sExpression balanced-filter number; n _aThe title number of filter that makes difficulties, n _a=n _s=P/2; M represents to extract number, and M=2m, m are natural number; L represents the length of analysis filterbank; Subscript-1 representing matrix contrary; The transposition of subscript T representing matrix; I _nExpression n rank unit matrix; J _nThe counter-rotating matrix of expression n rank unit matrix; Diag () represents diagonal matrix; z ^-1Represent a unit time-delay; W _2nThe expression butterfly structure,

Analysis filterbank and synthesis filter group all are linear phases;

The process of lattice structure synthesis filter set constructor method is: at first to the subband noise modeling, the subband noise model is described as a linear time invariant system, when the input signal of system was white noise, the spectrum of output signal was identical with the spectrum of subband noise n (k), and system function is designated as W _n(z); Determine a kind of heterogeneous components R (z) of lattice structure synthesis filter group of optimum again according to the lattice structure of the heterogeneous component E (z) of analysis filterbank, utilize the corresponding synthesis filter of heterogeneous components R (z) that original image x (n) is reconstructed then, obtain reconstructed image Reconstructed image Satisfy the power spectrum norm minimum of error signal e (n);

The heterogeneous component E (z) of the lattice structure analysis filterbank with linear phase of known transmitting terminal,

In the formula (1):

In the formula (2):

i＝1，2，…，k；

Be n _s* n _aInvertible matrix;

n＝P/2＝n _s＝n _a；

In the formula (3):

U ₀Be n _s* [M/2] but the left inverse matrix;

V ₀Be n _a* [M/2] but the left inverse matrix;

The system function of known subband noise model is W _n(z), then the heterogeneous components R (z) of Zui You lattice structure synthesis filter group is,

R(z)＝R _0opt(z)z ^-1G ₁ ^-1(z)…z ^-1G _k-1 ^-1(z)z ^-1G _k ^-1(z) (4)

In the formula (5):

X _1optBe [M/2] * n _sMatrix,

X _2optBe [M/2] * n _aMatrix,

In formula (7), (8):

Ψ ₁₁Be n _s* n _sInvertible matrix,

Ψ ₂₂Be n _a* n _aInvertible matrix,

U ₀Be n _s* [M/2] but the left inverse matrix,

V ₀Be n _a* [M/2] but the left inverse matrix.

2. the building method of lattice structure synthesis filter group according to claim 1 is characterized in that the power spectrum norm of described error signal e (n) is:

‖e‖ ₂＝‖R(z)W _n(z)‖ ₂ (9)。

3. the building method of lattice structure synthesis filter group according to claim 1 is characterized in that described Ψ ₁₁And Ψ ₂₂Be the block diagonal matrix of Ψ,

Ψ or try to achieve by following formula:

In the formula (10):

Φ is Lyapunov equation Φ-A Φ A ^T=BB ^TSeparate,

A, B, C, D are the state space variable of the corresponding system of transport function W (z),

W(z)＝z ^-1G ₁ ^-1(z)z ^-1G ₂ ^-1(z)…z ^-1G _k ^-1(z)W _n(z)，

W _n(z) be the system function of subband noise model,

W (z)=D+C * (zI-A) ^-1* B; Ψ or try to achieve by following formula:

In the formula (11):

W(z)＝z ^-1G ₁ ^-1(z)z ^-1G ₂ ^-1(z)…z ^-1G _k ^-1(z)W _n(z)＝W ₀+W ₁z ^-1+…+W _Nz ^-N (12)。

4. the building method of lattice structure synthesis filter group according to claim 1 is characterized in that the lattice structure performing step of heterogeneous component E (z) of described analysis filterbank is as follows:

(1) M group input signal is numbered 0 to M-1;

(2) M group input signal carries out butterfly computation;

(3) output signal that is obtained by step (2) multiply by coefficient 2 ^-1/2

(4) in the output signal that is obtained by step (3), be divided into two parts up and down in order, every part has m group signal, and the first half m group signal is through module U ₀, obtain n _sThe group output signal;

(5) in the output signal that is obtained by step (3), the latter half m group signal is through module V ₀, obtain n _aThe group output signal;

(6) n that obtains by step (4) _sGroup output signal and the n that obtains by step (5) _aGroup output signal P group output signal is altogether carried out butterfly computation, and the output signal behind the butterfly computation is divided into two parts up and down in order, and the first half has n _sThe group output signal, the latter half has n _aThe group output signal;

(7) in the output signal that obtains by step (6), the latter half n _aZ of unit of group output signal time-delay ^-1

(8) the first half n that obtains by step (6) _sGroup output signal and the n that obtains by step (7) _aGroup output signal P group output signal is altogether carried out butterfly computation;

(9) in the output signal that obtains by step (8), the first half n _sThe group signal is through module U ₁

(10) all P group output signals multiply by coefficient 1/2;

(11) step (6) to (10) is lattice structure G ₁(z) specific implementation step;

(12) through G ₁(z) signal will pass through G ₂(z) to G _k(z), G ₂(z) to G _k(z) and G ₁(z) structure is identical, just module U _iIn the parameter difference, i=1 wherein, 2 ..., k.

5. the building method of lattice structure synthesis filter group according to claim 1 is characterized in that the lattice structure performing step of heterogeneous components R (z) of described synthesis filter group is as follows:

(1) P group input signal is numbered 0 to P-1, passes through module z successively ^-1G _k ^-1(z) to z ^-1G ₂ ^-1(z);

(2) through module z ^-1G ₂ ^-1(z) output signal multiply by coefficient 1/2, and output signal is divided into two parts up and down in order, and the first half has n _sThe group output signal, the latter half has n _aThe group output signal;

(3) the first half n that obtains by step (2) _sThe group output signal is through module U ₁ ^-1

(4) the latter half n that obtains by step (2) _aGroup output signal and the n that obtains by step (3) _sGroup output signal P group output signal is altogether carried out butterfly computation, and the output signal behind the butterfly computation is divided into two parts up and down in order, and the first half has n _sThe group output signal, the latter half has n _aThe group output signal;

(5) the first half n that obtains by step (4) _sZ of unit of group output signal time-delay ^-1

(6) the latter half n that obtains by step (4) _aGroup output signal and the n that obtains by step (5) _sGroup output signal P group output signal is altogether carried out butterfly computation, and the output signal behind the butterfly computation is divided into two parts up and down in order, and the first half has n _sThe group output signal, the latter half has n _aThe group output signal;

(7) step (2) is lattice structure module z to step (6) ^-1G ₁ ^-1(z) specific implementation step;

(8) through z ^-1G ₁ ^-1(z) to pass through module z successively before the signal ^-1G _k ^-1(z) to z ^-1G ₂ ^-1(z), z ^-1G _k ^-1(z) to z ^-1G ₂ ^-1(z) and z ^-1G ₁ ^-1(z) structure is identical, just module U _i ^-1In the parameter difference, i=1 wherein, 2 ..., k;

(9) P that is obtained by step (6) organizes in the output signal, the first half n _sThe group output signal is through module X _1optObtain m group output signal afterwards;

(10) P that is obtained by step (6) organizes in the output signal, the latter half n _aThe group output signal is through module X _2optObtain m group output signal afterwards;

(11) all M=2m group output signals multiply by coefficient 2 ^-1/2

(12) output signal that is obtained by step (11) is carried out butterfly computation.

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