CN102545833A - Two-channel linear phase wavelet filter bank with two-level polyphase substructure - Google Patents

Abstract

The invention discloses an even-length two-channel linear phase wavelet filter bank with a two-level multi-phase substructure. In an analysis filter bank of the even-length two-channel linear phase wavelet filter bank, a polyphase substructure consisting of filters T0(z<2>), L1(z<2>), T1(z<2>) and L0(z<2>) is concatenated on a right side, and the other polyphase substructure is a special polyphase substructure of which all T0(z<2>), L0(z<2>) and L1(z<2>) are 1 and T1(z<2>) is -1, and is concatenated on a left side. In a comprehensive filter bank of the even-length two-channel linear phase wavelet filter bank, a polyphase substructure consisting of filters T1(z<2>), -L1(z<2>), T0(z<2>) and -L0(z<2>) is concatenated on the left side, and a polyphase substructure the same as the special polyphase substructure of the analysis filter bank is concatenated on the right side. The operating rate of the even-length two-channel linear phase wavelet filter bank can be the same as that of a wavelet filter bank with a polyphase structure, the number of multiplication operation times is about halved, and the shortcoming that a polyphase filter generally does not have a linear phase is overcome.

Description

A kind of two channel linear phase place wavelet filter groups with the heterogeneous minor structure of two-stage

Technical field

The present invention relates to the signal processing field, be specially a kind of even length two channel linear phase place wavelet filter groups with the heterogeneous minor structure of two-stage.

Background technology

Wavelet filter group (wavelet filter banks) is a kind of desirable reconstruction filter group (perfect reconstruction filter banks) that satisfies regularity (regularity), is widely used in the systems such as signal analysis and image encoding.The traditional structure of two passage wavelet filter groups is as shown in Figure 1, and it is by the analysis filter H of analysis filterbank ₀(z) and H ₁(z), the synthesis filter F of withdrawal device, null value interpolater and synthesis filter group ₀(z) and F ₁(z) constitute.With analysis filter H ₀(z) and H ₁(z) and synthesis filter F ₀(z) and F ₁(z) carry out heterogeneous decomposition; Can convert the traditional structure of two passage wavelet filter groups into heterogeneous structure (polyphase structure) with universal method again; Referring to document 1 (P.P.Vaidyanathan; Multirate Systems and Filter Banks.Englewood Cliffs, NJ:Prentice-Hall, 1993.).Because the multiphase filter in the heterogeneous structure all walks abreast; And length is merely half the before the heterogeneous decomposition; Thereby the arithmetic speed of heterogeneous structure wavelet filter group is the twice of traditional structure wavelet filter group, and this requires the application in field significant to promoting the wavelet filter group at high real-time.Two passage wavelet filter groups are odd number or even number by its filter length, can be divided into two types of strange length and even length again.Two channel linear phase place wavelet filter groups of strange length; Its all multiphase filters all have linear phase, and two channel linear phase place wavelet filter groups of even length, its multiphase filter does not generally have linear phase; Thereby when realizing, the multiplying number of times is wanted many one times.The heterogeneous structure of two channel linear phase place wavelet filter groups of idol length is as shown in Figure 2, E among the figure ₀(z) and

It is filters H ₀(z) multiphase filter, E ₁(z) and It is filters H ₁(z) multiphase filter.Except heterogeneous structure, two channel linear phase place wavelet filter groups of even length also have two kinds of structures at present, and a kind of is lattice structure (lattice structure); Referring to document 2 (Park, S.Y.and Cho, N.I.; " Design of multiplierless lattice QMF:structure and algorithm development, " IEEE Trans.Circuits Syst.II, Analog Digit.Signal Process.Express Briefs.vol.55 no.2; Pp173-177; Feb.2008.), another kind is trapezoidal-structure (lifting structure), referring to document 3 (Zhang Lei and Anamitra Makur; " Structurally linear phase factorization of 2-channel filter banks based on lifting "; ICASSP2005, IV, pp.609-612).These two kinds of structures are all formed by multistage heterogeneous minor structure cascade, and linear phase and desirable (perfect reconstruction) characteristic of rebuilding, the word length effects that not quantized by filter coefficient.Exactly because but formed by multistage heterogeneous minor structure cascade, thereby the arithmetic speed of these two kinds of structures is all obviously lower than the heterogeneous structure.And the method for still not having at present a simple, general-purpose converts the heterogeneous structure of two channel linear phase place wavelet filter groups of even length to this two kinds of structures.Another characteristic of wavelet filter group is regularity (regularity), and it is through H ₀(z) at the zero point and the H at z=-1 place ₁(z) obtain at the zero point at z=1 place.The no matter traditional structure or the heterogeneous structure of wavelet filter group, its regularity all will change after the wavelet filter group realizes, and this is because the quantification word length effects of filter coefficient, analysis filter H ₀(z) at the zero point and the H at z=-1 place ₁(z) all disturbance will take place at the zero point at z=1 place, make H ₀(z=1) and H ₁(z=1) all non-vanishing.Thereby after in image processing, causing compressed image to recover, block disturb (checkerboarding) appears.

Therefore, seek a kind of even length two channel linear phase place wavelet filter groups with the heterogeneous minor structure of two-stage, its arithmetic speed is identical with heterogeneous structure wavelet filter group, but the minimizing of multiplying number of times is near half the, and structurally guarantees H ₀And H (z=1)=0 ₁(z=1)=0, obviously has realistic meaning in low-power consumption and real-time demanding field application.

Summary of the invention

The object of the present invention is to provide a kind of even length two channel linear phase place wavelet filter groups with the heterogeneous minor structure of two-stage; Compared with prior art: arithmetic speed is identical with heterogeneous structure wavelet filter group, but the multiplying number of times is closely more half the than the minimizing of heterogeneous structure wavelet filter group; H ₀And H (z=1)=0 ₁(z=1)=0 this characteristic is that structure is intrinsic, does not receive the quantification word length effects of filter coefficient; The method that simple, general-purpose is arranged; Convert the heterogeneous structure of two channel linear phase place wavelet filter groups of even length to this wavelet filter group structure provided by the invention; Thereby both can efficiently realize, can overcome the shortcoming that its multiphase filter does not generally have linear phase again.

The object of the invention is realized through following technical proposals: a kind of even length two channel linear phase place wavelet filter groups with the heterogeneous minor structure of two-stage; Constitute by analysis filterbank, withdrawal device, null value interpolater and synthesis filter group; It is characterized in that: the heterogeneous structure of analysis filterbank and synthesis filter group is all formed by two heterogeneous minor structure cascades respectively; A heterogeneous minor structure is two inputs, two output filter modules; Another heterogeneous minor structure is special two inputs, two output modules, and in analysis filterbank, two inputs, two output filter modules are by filter T ₀(z ²), L ₁(z ²), T ₁(z ²) and L ₀(z ²) constitute, special two inputs, two output modules are T ₀(z ²)=1, L ₀(z ²)=1, L ₁(z ²)=1 and T ₁(z ²1 o'clock a kind of special two inputs, two output filter modules of)=-; Its first output [7] is connected in the first input end [1] of two inputs, two output filter modules; Its second output [8] is connected in second input [2] of two inputs, two output filter modules; Its first input end [5] is connected in the input [9] of wavelet filter group [30], and its second input [6] is connected in delay cell z ^-1[10] output, delay cell z ^-1[10] input is connected in the input [9] of wavelet filter group [30], thereby constitutes by analysis filter H ₀(z) and H ₁The heterogeneous structure of the analysis filterbank of (z) forming; In the synthesis filter group, two inputs, two output filter modules are by filter T ₁(z ²) ,-L ₁(z ²), T ₀(z ²) and-L ₀(z ²) constitute; Special two inputs, two output modules are identical with analysis filterbank; Its first input end [15] is connected in first output [13] of two inputs, two output filter modules; Its second input [16] is connected in second output [14] of two inputs, two output filter modules, and its first output [17] is connected in delay cell z ^-1[20] input, its second output [18] is connected in the output [19] of wavelet filter group [30], delay cell z ^-1[20] output is connected in the output [19] of wavelet filter group [30], thereby constitutes by synthesis filter F ₀(z) and F ₁The heterogeneous structure of the synthesis filter group of (z) forming.

Owing to adopted said structure, thereby realized following relation:

1) relation of analysis filterbank and the heterogeneous minor structure of its two-stage does

$\left[\begin{array}{c}{H}_0\left(z\right)\\ H_1\left(z\right)\end{array}\right]=\left[\begin{array}{cc}{T}_0\left(z^2\right)& L_0\left(z^2\right)\\ L_1\left(z^2\right)& T_1\left(z^2\right)\end{array}\right]\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right]\left[\begin{array}{c}1\\ z^{-1}\end{array}\right]---\left(1\right)$

2) relation of synthesis filter group and the heterogeneous minor structure of its two-stage does

$\left[\begin{array}{cc}{F}_0\left(z\right)& F_1\left(z\right)\end{array}\right]=\left[\begin{array}{cc}{z}^{-1}& 1\end{array}\right]\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right]\left[\begin{array}{cc}{T}_1\left(z^2\right)& -L_0\left(z^2\right)\\ -L_1\left(z^2\right)& T_0\left(z^2\right)\end{array}\right]---\left(2\right)$

3) relation of the multiphase filter of even length two channel linear phase place wavelet filter groups and two inputs, two output filter module median filters does

$\left[\begin{array}{cc}{T}_0\left(z\right)& L_0\left(z\right)\\ L_1\left(z\right)& T_1\left(z\right)\end{array}\right]=\frac{1}{2}\left[\begin{array}{cc}{E}_0\left(z\right)+{\tilde{E}}_0\left(z\right)& E_0\left(z\right)-{\tilde{E}}_0\left(z\right)\\ E_1\left(z\right)-{\tilde{E}}_1\left(z\right)& E_1\left(z\right)+{\tilde{E}}_1\left(z\right)\end{array}\right]---\left(3\right)$

E wherein ₀(z) and

It is filters H ₀(z) multiphase filter, its length is N ₀/ 2, E ₁(z) and It is filters H ₁(z) multiphase filter, its length is N ₁/ 2, promptly

4) the filter T after two times of extractions of two input two output filter modules ₀(z), T ₁(z), L ₀(z) and L ₁(z) relation between is specially

T ₀(z)T ₁(z)-L ₀(z)L ₁(z)＝z ^-k/4 (4)

K=(N wherein ₀+ N ₁)/4-1, N ₀And N ₁Be respectively filters H ₀(z) and filters H ₁(z) length.

Because filters H ₀(z) even symmetry, filters H ₁(z) odd symmetry, thereby E ₀(z) with

Multinomial coefficient identical, but it is opposite to put in order, E ₁(z) and

Multinomial coefficient also identical, it is also opposite to put in order.So (3) formula is established: filter T ₀(z) and T ₁(z) be even symmetry, filter L ₀(z) and L ₁(z) be odd symmetry.Obviously, all filters all have this characteristic of linear phase in two inputs, the two output filter modules, are that wavelet filter group of the present invention is structurally intrinsic.Because (3) formula shows two inputs, two output filter module median filter T ₀(z) and L ₀(z) length and filters H ₀(z) multiphase filter E ₀(z) and

Length identical, filter T ₁(z) and L ₁(z) length and filters H ₁(z) multiphase filter E ₁(z) and

Length identical, so among Fig. 3 among arithmetic speed and Fig. 2 of two inputs, two output filter modules by multiphase filter E ₀(z) and

And multiphase filter E ₁(z) and

The arithmetic speed of the heterogeneous structure module that constitutes is identical.Add since among Fig. 3 special two inputs do not have delay cell in two output modules, thereby the arithmetic speed of wavelet filter group of the present invention and heterogeneous structure wavelet filter group is identical.Because all filters all have linear phase in two inputs, the two output filter modules; And the multiphase filter in the heterogeneous structure module does not generally have linear phase; The computing of adding special two inputs, two output modules among Fig. 3 only comprises twice add operation and does not have multiplying; So the arithmetic speed of wavelet filter group of the present invention is identical with heterogeneous structure wavelet filter group, but the multiplying number of times is closely more half the than the minimizing of heterogeneous structure wavelet filter group.Because filter L ₀(z) and L ₁(z) be odd symmetry, so L ₀And L (z=1)=0 ₁(z=1)=0.Thereby can be by (1) formula and (2) formula checking H ₀And H (z=1)=0 ₁And F (z=1)=0 ₀And F (z=1)=0 ₁(z=1)=0 this characteristic is that wavelet filter group of the present invention is structurally intrinsic, does not receive filter T ₀(z ²), L ₀(z ²), T ₁(z ²) and L ₁(z ²) filter coefficient quantize the word length effects.Because (3) formula has comprised the relation that the multiphase filter and two of two channel linear phase place wavelet filter groups of even length is imported two output filter module median filters; So heterogeneous structure of two channel linear phase place wavelet filter groups of existing even length; The method of available simple, general-purpose; I.e. (3) formula, the structure of conversion cost invention wavelet filter group.

In sum; The invention has the beneficial effects as follows: all filters all have linear phase in two inputs, the two output filter modules; Thereby wavelet filter group of the present invention; Arithmetic speed is identical with heterogeneous structure wavelet filter group, but the multiplying number of times is closely more half the than the minimizing of heterogeneous structure wavelet filter group; H ₀And H (z=-1)=0 ₁(z=1)=0 this characteristic is that structure is intrinsic, thereby the structurally intrinsic single order vanishing moment of wavelet filter group of the present invention (vanishing moments); Because (3) formula has comprised the conversion method of wavelet filter group of the present invention; So heterogeneous structure of two channel linear phase place wavelet filter groups of existing even length; All can be according to the structure of (3) formula conversion cost invention wavelet filter group; Thereby efficient the realization, and overcome the shortcoming that its multiphase filter does not generally have linear phase.

Description of drawings

Fig. 1 is the traditional structure block diagram of existing two passage wavelet filter groups

Fig. 2 is the heterogeneous structure block diagram of two channel linear phase place wavelet filter groups of existing even length

Fig. 3 is the structured flowchart of wavelet filter group of the present invention

Embodiment

Do further explain below in conjunction with accompanying drawing and embodiment, but execution mode of the present invention is not limited only to this.

Fig. 3 is a kind of structured flowchart with even length two channel linear phase place wavelet filter groups of the heterogeneous minor structure of two-stage provided by the invention, and this wavelet filter group is called [30].Wavelet filter group [30]; The heterogeneous structure of its analysis filterbank and synthesis filter group is all formed by two heterogeneous minor structure cascades respectively; A heterogeneous minor structure is two inputs, two output filter modules, and another heterogeneous minor structure is special two inputs, two output modules.In analysis filterbank, two inputs, two output filter modules are by filter T ₀(z ²), L ₁(z ²), T ₁(z ²) and L ₀(z ²) constitute, its first input end [1] is connected in filter T ₀(z ²) input and the filter L of [21] ₁(z ²) input, its second input [2] is connected in filter T ₁(z ²) input and the filter L of [22] ₀(z ²) input, its first output [3] is connected in filter T ₀(z ²) output and the filter L of [21] ₀(z ²) output, its second output [4] is connected in filter T ₁(z ²) output and the filter L of [22] ₁(z ²) output; Special two inputs, two output modules are T ₀(z ²)=1, L ₀(z ²)=1, L ₁(z ²)=1 and T ₁(z ²1 o'clock a kind of special two inputs, two output filter modules of)=-; Its first output [7] is connected in the first input end [1] of two inputs, two output filter modules; Its second output [8] is connected in second input [2] of two inputs, two output filter modules; Its first input end [5] is connected in the input [9] of wavelet filter group [30], and its second input [6] is connected in delay cell z ^-1[10] output, delay cell z ^-1[10] input is connected in the input [9] of wavelet filter group [30].The input of withdrawal device [25] is connected in first output [3] of two inputs, two output filter modules, and the input of withdrawal device [26] is connected in second output [4] of two inputs, two output filter modules.In the synthesis filter group, two inputs, two output filter modules are by filter T ₁(z ²) ,-L ₁(z ²), T ₀(z ²) and-L ₀(z ²) constitute, its first input end [11] is connected in filter T ₁(z ²) input and the filter-L of [23] ₁(z ²) input, its second input [12] is connected in filter T ₀(z ²) input and the filter-L of [24] ₀(z ²) input, its first output [13] is connected in filter T ₁(z ²) output and the filter-L of [23] ₀(z ²) output, its second output [14] is connected in filter T ₀(z ²) output and the filter-L of [24] ₁(z ²) output; Special two inputs, two output modules are identical with analysis filterbank; Its first input end [15] is connected in first output [13] of two inputs, two output filter modules; Its second input [16] is connected in second output [14] of two inputs, two output filter modules, and its first output [17] is connected in delay cell z ^-1[20] input, its second output [18] is connected in the output [19] of wavelet filter group [30], delay cell z ^-1[20] output is connected in the output [19] of wavelet filter group [30].The output of null value interpolater [27] is connected in the first input end [11] of two inputs, two output filter modules, and the output of null value interpolater [28] is connected in second input [12] of two inputs, two output filter modules.The signal of the output of withdrawal device [25] output is input to the input of null value interpolater [27], and the signal of the output output of withdrawal device [26] is input to the input of null value interpolater [28].

Because two channel linear phase place wavelet filter groups of even length have ripe method for designing, so no longer detail in the present invention.As long as confirm filters H ₀(z) and H ₁(z) symmetry, length and vanishing moment (vanishing moments) exponent number, promptly available existing method for designing is tried to achieve filters H ₀(z) and H ₁(z), thus try to achieve multiphase filter E ₀(z) and

And E ₁(z) and

Can try to achieve the filter T after two input two output filter modules two times of extractions by (3) formula again ₀(z), L ₀(z), T ₁(z) and L ₁(z), filter F ₀(z) and F ₁(z) can try to achieve according to (2) formula.In the two channel linear phase place wavelet filter groups of idol length, filters H ₀(z) be even symmetry, filters H ₁(z) be odd symmetry, filters H ₀(z) length is used N ₀Expression, filters H ₁(z) length is used N ₁Expression, and N ₁=N ₀+ 4m (m is an integer), vanishing moment (vanishing moments) exponent number represent that with P P confirms according to actual conditions.

Embodiment one

Confirm N ₀=6, N ₁=10, P=3 can obtain filters H with existing method for designing ₀(z) and H ₁(z) do

h ₀＝[-1/16，1/16，1/2，1/2，1/16，-1/16]

(5)

h ₁＝[1/128，-1/128，-1/16，-1/16，31/64，-31/64，1/16，1/16，1/128，-1/128]

Try to achieve filter E by (5) formula ₀(z),

E ₁(z) and For

e ₀＝[-1/16，1/2，1/16]

${\tilde{e}}_0=[1/\mathrm{16,1}/2,-1/16]$

(6)

e ₁＝[1/128，-1/16，31/64，1/16，1/128]

${\tilde{e}}_1=[1/\mathrm{128,1}/\mathrm{16,31}/64,-1/\mathrm{16,1}/128]$

(6) formula shows E ₀(z) with Multinomial coefficient identical, but it is opposite to put in order; E ₁(z) with

Multinomial coefficient also identical, it is also opposite to put in order.Try to achieve the filter T after two times of extractions of two input two output filter modules by (6) formula and (3) formula ₀(z), L ₀(z), T ₁(z) and L ₁(z) do

t ₀＝[0，1/2，0]

l ₀＝[-1/16，0，1/16]

(7)

t ₁＝[1/128，0，31/64，0，1/128]

l ₁＝[0，-1/16，0，1/16，0]

(7) formula shows in the input of two after the two times of extractions two output filter modules: filter T ₀(z) and T ₁(z) be even symmetry; Filter L ₀(z) and L ₁(z) be odd symmetry; L ₀And L (z=1)=0 ₁(z=1)=0; T ₀(z) T ₁(z)-L ₀(z) L ₁(z)=z ^-3/ 4.

In this example, (5) formula shows in the wavelet filter group of traditional structure: filters H ₀(z) convolution algorithm need be accomplished 2 multiplyings, 5 sub-addition computings, filters H ₁(z) convolution algorithm need be accomplished 3 multiplyings, 9 sub-addition computings; (6) formula shows in the wavelet filter group of heterogeneous structure: multiphase filter E ₀(z) and

All do not have linear phase, the filters H of heterogeneous structure ₀(z) convolution algorithm need be accomplished 4 multiplyings, 5 sub-addition computings, multiphase filter E ₁(z) and

All do not have linear phase, the filters H of heterogeneous structure ₁(z) convolution algorithm need be accomplished 6 multiplyings, 9 sub-addition computings; (7) formula shows in two inputs, the two output filter modules: filter T ₀(z ²) and L ₀(z ²) all have linear phase, a filters H ₀(z) convolution algorithm need be accomplished 2 multiplyings, 3 sub-addition computings, filter L ₁(z ²) and T ₁(z ²) all have linear phase, a filters H ₁(z) convolution algorithm need be accomplished 3 multiplyings, 5 sub-addition computings.Because special two inputs do not have delay cell in two output modules, so the arithmetic speed of this routine wavelet filter group and heterogeneous structure wavelet filter group is identical.Also owing to special two inputs, two output modules only have twice add operation and do not have multiplying in computing; So the multiplying number of times of this routine wavelet filter group is more half the than the minimizing of heterogeneous structure wavelet filter group, the add operation number of times is than the minimizing 3/7ths of heterogeneous structure wavelet filter group.The multiplying number of times of this routine wavelet filter group is identical with traditional structure wavelet filter group, but the add operation number of times is than the minimizing 3/7ths of traditional structure wavelet filter group, and arithmetic speed is the twice of traditional structure wavelet filter group.Because L ₀And L (z=1)=0 ₁(z=1)=0, thus be not difficult basis (1) formula and the checking of (2) formula, H ₀And H (z=1)=0 ₁And F (z=1)=0 ₀And F (z=1)=0 ₁(z=1)=0, i.e. the structurally intrinsic single order vanishing moment of this routine wavelet filter group.

Embodiment two

Confirm N ₀=8, N ₁=12, P=3 can obtain filters H with existing method for designing ₀(z) and H ₁(z) do

h ₀＝[1/32，-1/32，1/32，15/32，15/32，1/32，-1/32，1/32]

(8)

h ₁＝[1，-1，-7，23，22，-134，134，-22，-23，7，1，-1]/256

Try to achieve filter E by (8) formula ₀(z),

E ₁(z) and

For

e ₀＝[1/32，1/32，15/32，-1/32]

${\tilde{e}}_0=[-1/\mathrm{32,15}/\mathrm{32,1}/\mathrm{32,1}/32]$

(9)

e ₁＝[1/256，-7/256，11/128，67/128，-23/256，1/256]

${\tilde{e}}_1=[1/256,-23/\mathrm{256,67}/\mathrm{128,11}/128,-7/\mathrm{256,1}/256]$

(9) formula shows E ₀(z) with

E ₁(z) with

Multinomial coefficient is identical, but it is opposite to put in order.Try to achieve the filter T after two times of extractions of two input two output filter modules by (9) formula and (3) formula ₀(z), L ₀(z), T ₁(z) and L ₁(z) do

t ₀＝[0，1/4，1/4，0]

l ₀＝[1/32，-7/32，7/32，-1/32]

(10)

t ₁＝[1/256，-15/256，39/128，39/128，-15/256，1/256]

l ₁＝[0，1/32，-7/32，7/32，-1/32，0]

(10) formula shows in the input of two after the two times of extractions two output filter modules: filter T ₀(z) and T ₁(z) be even symmetry, filter L ₀(z) and L ₁(z) be odd symmetry; L ₀And L (z=1)=0 ₁(z=1)=0; T ₀(z) T ₁(z)-L ₀(z) L ₁(z)=z ^-4/ 4.

In this example, (8) formula shows in the wavelet filter group of traditional structure: filters H ₀(z) convolution algorithm need be accomplished 2 multiplyings, 7 sub-addition computings, filters H ₁(z) convolution algorithm need be accomplished 5 multiplyings, 11 sub-addition computings; (9) formula shows in the wavelet filter group of heterogeneous structure: multiphase filter E ₀(z) and

All do not have linear phase, the filters H of heterogeneous structure ₀(z) convolution algorithm need be accomplished 4 multiplyings, 7 sub-addition computings, multiphase filter E ₁(z) and

All do not have linear phase, the filters H of heterogeneous structure ₁(z) convolution algorithm need be accomplished 10 multiplyings, 11 sub-addition computings; (10) formula shows in two inputs, the two output filter modules: filter T ₀(z ²) and L ₀(z ²) all have linear phase, a filters H ₀(z) convolution algorithm need be accomplished 3 multiplyings, 6 sub-addition computings, filter L ₁(z ²) and T ₁(z ²) all have linear phase, a filters H ₁(z) convolution algorithm need be accomplished 5 multiplyings, 10 sub-addition computings.Compare with the wavelet filter group of heterogeneous structure; The arithmetic speed of this routine wavelet filter group is identical with heterogeneous structure wavelet filter group; But the multiplying number of times is than the minimizing 3/7ths of heterogeneous structure wavelet filter group, and the add operation number of times is than the minimizing 1/9th of heterogeneous structure wavelet filter group.Compare with the wavelet filter group of traditional structure, the multiplying number of times of this routine wavelet filter group manys once than traditional structure wavelet filter group, but the add operation number of times reduces 1/9th, and arithmetic speed is the twice of traditional structure wavelet filter group.Because L ₀And L (z=1)=0 ₁(z=1)=0, so can verify the structurally intrinsic single order vanishing moment of this routine wavelet filter group according to (1) formula and (2) formula.

Above embodiment result shows: wavelet filter group of the present invention; Arithmetic speed is identical with heterogeneous structure wavelet filter group; But the multiplying number of times is closely more half the than the minimizing of heterogeneous structure wavelet filter group; And structurally intrinsic single order vanishing moment (vanishing moments), and with regard to the foregoing description, the add operation number of times is lacking than heterogeneous structure wavelet filter group also; The heterogeneous structure of two channel linear phase place wavelet filter groups of existing even length; The structure of the method conversion cost invention wavelet filter group of available simple, general-purpose; Thereby both can efficiently realize, can overcome the shortcoming that its multiphase filter does not generally have linear phase again.Thereby has a good application prospects.

Claims (7)

1. even length two channel linear phase place wavelet filter groups with the heterogeneous minor structure of two-stage; Constitute by analysis filterbank, withdrawal device, null value interpolater and synthesis filter group; It is characterized in that: the heterogeneous structure of analysis filterbank and synthesis filter group is all formed by two heterogeneous minor structure cascades respectively; A heterogeneous minor structure is two inputs, two output filter modules; Another heterogeneous minor structure is special two inputs, two output modules, and in analysis filterbank, two inputs, two output filter modules are by filter T ₀(z ²), L ₁(z ²), T ₁(z ²) and L ₀(z ²) constitute, special two inputs, two output modules are T ₀(z ²)=1, L ₀(z ²)=1, L ₁(z ²)=1 and T ₁(z ²1 o'clock a kind of special two inputs, two output filter modules of)=-; Its first output [7] is connected in the first input end [1] of two inputs, two output filter modules; Its second output [8] is connected in second input [2] of two inputs, two output filter modules; Its first input end [5] is connected in the input [9] of wavelet filter group [30], and its second input [6] is connected in delay cell z ^-1[10] output, delay cell z ^-1[10] input is connected in the input [9] of wavelet filter group [30], thereby constitutes by analysis filter H ₀(z) and H ₁The heterogeneous structure of the analysis filterbank of (z) forming; In the synthesis filter group, two inputs, two output filter modules are by filter T ₁(z ²) ,-L ₁(z ²), T ₀(z ²) and-L ₀(z ²) constitute; Special two inputs, two output modules are identical with analysis filterbank; Its first input end [15] is connected in first output [13] of two inputs, two output filter modules; Its second input [16] is connected in second output [14] of two inputs, two output filter modules, and its first output [17] is connected in delay cell z ^-1[20] input, its second output [18] is connected in the output [19] of wavelet filter group [30], delay cell z ^-1[20] output is connected in the output [19] of wavelet filter group [30], thereby constitutes by synthesis filter F ₀(z) and F ₁The heterogeneous structure of the synthesis filter group of (z) forming.

2. wavelet filter group according to claim 1 is characterized in that, the structure of two in analysis filterbank input, two output filter modules is specially, first input end [1] respectively with filter T ₀(z ²) input and the filter L of [21] ₁(z ²) input be connected, second input [2] respectively with filter T ₁(z ²) input and the filter L of [22] ₀(z ²) input be connected, first output [3] respectively with filter T ₀(z ²) output and the filter L of [21] ₀(z ²) output be connected, second output [4] respectively with filter T ₁(z ²) output and the filter L of [22] ₁(z ²) output be connected.

3. wavelet filter group according to claim 1 is characterized in that, the structure of two in synthesis filter group input, two output filter modules is specially, first input end [11] respectively with filter T ₁(z ²) input and the filter-L of [23] ₁(z ²) input be connected, second input [12] respectively with filter T ₀(z ²) input and the filter-L of [24] ₀(z ²) input be connected, first output [13] respectively with filter T ₁(z ²) output and the filter-L of [23] ₀(z ²) output be connected, second output [14] respectively with filter T ₀(z ²) output and the filter-L of [24] ₁(z ²) output be connected.

4. wavelet filter group according to claim 1 is characterized in that, the structurally intrinsic single order vanishing moment of this wavelet filter group.

5. two inputs, two output filter modules according to claim 1 and 2 is characterized in that the relation between the multiphase filter of two channel linear phase place wavelet filter groups of filter in the above-mentioned filter module and even length is specially,

。

6. two inputs, two output filter modules according to claim 5 is characterized in that the filter after two times of extractions of above-mentioned filter module all has linear phase, and its symmetry is specially, filter T ₀(z) and T ₁(z) be even symmetry, filter L ₀(z) and L ₁(z) be odd symmetry.

7. two inputs, two output filter modules according to claim 6 is characterized in that the filter T after two times of extractions of above-mentioned filter module ₀(z), T ₁(z), L ₀(z) and L ₁(z) relation between is specially T ₀(z) T ₁(z)-L ₀(z) L ₁(z)=z ^-k/ 4.

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