CN110061717A - The two channel quadrature mirror filter group design methods based on iterative gradient search - Google Patents
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Abstract
The present invention provides a kind of two channel quadrature mirror filter group design methods based on iterative gradient search.The non-convex optimization problem of script nonlinearity is changed into convex optimization problem and is iterated solution by it using iterative gradient search (IGS, iterative gradient searching) technology.The method that we invent is compared with previous methods, it is no longer limited to solve the objective function that some is fixed, it can be according to the needs of design, flexible change objective function, objective function can not only be expressed as to the form of criterion of least squares, additionally it is possible to be directly realized by the expression-form of minimum maximization criterion.And our method is compared with domestic and international other methods, and the normal selection of ptototype filter iteration initial coefficients has little influence on simulation result, and performance of filter index obtained has more superiority.
Description
Technical field
The invention belongs to digital signal processing technique fields, and in particular to a kind of two based on iterative gradient search technique are logical
Road quadrature mirror filter group design method.
Background technique
Two channel quadrature mirror filter groups (QMFB, quadrature mirror filter bank) are answered in recent years
For more and more fields, such as the sub-band coding of voice and picture signal, wavelet kernel etc..Due to answering extensively for QMFB
With people also increasingly pay attention to its design concern.The design method for the QMFB with LP and NPR characteristic having proposed is non-
Chang Duo is considered as based on the design method under criterion of least squares and minimum maximization criterion.
Most traditional design method is the method for Johnston, he proposes the weighting reconstructed error energy and stopband energy
Objective function is optimized with as objective function and using Hooke and Jeaves algorithm.Due to this target letter
Number is the biquadratic function about ptototype filter coefficient, which is nonlinearity and non-convex, is not easy to solve.It is based on
The method of Johnston, Jain and Crochiered et al. proposition solve this objective function by time domain formula.It
Afterwards, Chen and Lee proposes a kind of linearization technique the solution of this objective function is made to become simply, to reduce calculating
Complexity, and weighted least-squares (WLS, weighted least-squares) algorithm is combined, so that the integrative reconstruction of QMFB
Error is minimized in the minimum greatly meaning of entire frequency band.But since the ptototype filter coefficient of this method is to pass through calculating
The analytic solutions that the equation as composed by approximate matrix inversion and matrix multiplication directly obtains, and matrix inversion inherently have it is higher
Computation complexity, in addition, due to filter length height, it is also possible to will lead to the case where there is no matrix inversions.
Since the optimization process of analytic solutions can not directly give expression to the form of minimum maximization, in existing design side
In method, to obtain the QMFB with the moire behaviors such as reconstructed error or stopband attenuation, generally use be all WLS or it is improved
WLS method is obtained without being based on directly on minimum maximization criterion.Such as Y.C.Lim and C.K.Goh and Y.C.Lim et al.
It is all that the equal ripples QMFB under minimax meaning is generated using criterion of least squares by selecting weighting function appropriate.
Summary of the invention
The purpose of the present invention is to provide a kind of two channel quadrature mirror filter groups designs based on iterative gradient search
Method.
The present invention is specific as follows:
Step 1: according to design requirement, the order of frequency points L on Whole frequency band, linear phase ptototype filter is determined
N, stopband cutoff frequency fs.
Low-pass filter full rate matrix U is determined respectively by formula (1a), (1b), (1c)t, stop-band frequency matrix UsAnd height
Bandpass filter full rate matrix UT, (w+ π)。
Ut=[c (w1),...,c(ws),...,c(wL)]T (1a)
Us=[c (ws),c(ws+1),...,c(wL)]T (1b)
UT, (w+ π)=[c (w1+π),...,c(ws+π),...,c(wL+π)]T (1c)
In formula (1), wsIndicate stopband cutoff frequency point.
Step 2: setting iteration step length ε, iteration ends coefficient ε1, ptototype filter iteration initial coefficientsK is assigned to by 1.
QMFB lowpass analysis filter H under kth time iteration is obtained Step 3: solving0(w) filter coefficient
3-1. calculates the reconstructed error of QMFB obtained by -1 iteration of kthAs shown in formula (2).
In formula (2), " " representing matrix dot product.
3-2. is defined shown in a series of constant arrays such as formula (3).
3-3. calculates the resulting QMFB reconstructed error of -1 iteration of kthAbout coefficientFirst-order partial derivativeAs shown in formula (4).
The reconstructed error of QMFB when 3-4. calculates kth time iterationAs shown in formula (5).
In formula (5),Represent QMFB lowpass analysis filter H when kth time iteration0(w) coefficient increment.
The stopband attenuation of QMFB when kth time iterationAs shown in formula (6).
3-5. determines filter coefficient increment according to one of following nine kinds of methodsSize.
Method one: being solved according to the convex optimization problem that formula (7) are expressed, and determines the coefficient increment of kth time iteration
In formula (7), | | | |∞Indicate Infinite Norm operation, | | | |2Indicate 2 norm operations.δ needs minimize
Intermediate variable；σ indicates stopband maximum attenuation desired value, and α is weight coefficient.
Method two: the formula (7b) in method one is replaced with formula (7e), and determines the coefficient increment of kth time iteration
Method three: the formula (7b) in method one is replaced with formula (7f), and determines the coefficient increment of kth time iteration
Method four: the formula (7b) in method one is replaced with formula (7g), and determines the coefficient increment of kth time iteration
Method five: the formula (7b) in method one is replaced with formula (7h), and determines the coefficient increment of kth time iteration
Method six: formula (7c) this constraint condition in minimizing technology one determines the coefficient increment of kth time iteration
Method seven: formula (7c) this constraint condition in minimizing technology two determines the coefficient increment of kth time iteration
Method eight: formula (7c) this constraint condition in minimizing technology three determines the coefficient increment of kth time iteration
Method nine: formula (7c) this constraint condition in minimizing technology four determines the coefficient increment of kth time iteration
3-6. calculates kth time iterative filter coefficient
Step 4: k is increased 1, and repeat step 3 if formula (8) is invalid.It, will if formula (8) is set upMake
The QMFB lowpass analysis filter H gone out for final design0(w) coefficient.In same secondary design, step 3 determines coefficient increment
Using the same method.
In formula (8), δkIt is the δ that the formula (7) in kth time iteration determines.δk-1It is formula (7) determination in -1 iteration of kth
δ。
Further, in step 2, ptototype filter iteration initial coefficientsValue is [0,0 ..., 0,0.5]TOr it is logical
It crosses Parks-McClellan method or Direct Design Method obtains.
Further, in step 2, iteration step length ε=1.
Further, in step 2, iteration ends coefficient ε1=10-3。
Further, in the method one, two, six, seven, nine of step 3-5, the value of weight coefficient α is 1；In method three, power
The value of value coefficient α is 0.1；In method four, the value of weight coefficient α is 0.01；In method eight, the value of weight coefficient α is
0.5。
The invention has the advantages that:
The present invention can be no longer limited to optimize the objective function that some is fixed, can be according to design
It needs, flexibly changes objective function, objective function can not only be expressed as to the form of criterion of least squares, additionally it is possible to is directly real
The expression-form of existing minimum maximization criterion.And the present invention is compared with other methods, ptototype filter iteration initial coefficients
Normal choose has little influence on simulation result, and performance of filter index obtained has more superiority.
Detailed description of the invention
Fig. 1 is design flow diagram of the invention.
The QMFB amplitude-frequency response figure that Fig. 2 is drawn by the coefficient in table 1.
Fig. 3 is the QMFB reconstructed error frequency response chart that is drawn by the coefficient in table 1.
The QMFB amplitude-frequency response figure that the coefficient that Fig. 4 is obtained by the method for the present invention three is drawn.
The QMFB reconstructed error frequency response chart that the coefficient that Fig. 5 is obtained by the method for the present invention three is drawn.
The QMFB amplitude-frequency response figure that the coefficient that Fig. 6 is obtained by the method for the present invention four is drawn.
The QMFB reconstructed error frequency response chart that the coefficient that Fig. 7 is obtained by the method for the present invention four is drawn.
Specific embodiment
Below in conjunction with attached drawing, the invention will be further described.
As shown in Figure 1, the specific steps of the two channel quadrature mirror filter group design methods based on iterative gradient search
It is as follows:
Step 1: according to design requirement, determine frequency points L on Whole frequency band, linear phase ptototype filter (usually I
Also by lowpass analysis filter H0(w) be known as ptototype filter) order N (order N be even number), stopband cutoff frequency fs.
Low-pass filter full rate matrix U is determined respectively by formula (1a), (1b), (1c)t, stop-band frequency matrix UsAnd height
Bandpass filter full rate matrix UT, (w+ π)。
Ut=[c (w1),...,c(ws),...,c(wL)]T (1a)
Us=[c (ws),c(ws+1),...,c(wL)]T (1b)
UT, (w+ π)=[c (w1+π),...,c(ws+π),...,c(wL+π)]T (1c)
In formula (1a), (1b) and (1c), w1,w2,...,ws,...,wLIndicate a series of equally spaced discrete point in frequency in [0, π], wsIndicate resistance
With cutoff frequency point (Frequency point where stopband cutoff frequency fs).
Step 2: setting iteration step length ε, iteration ends coefficient ε1, ptototype filter iteration initial coefficients Value is [0,0 ..., 0,0.5]TOr it by Parks-McClellan method or directly sets
Meter method obtains.The corresponding the number of iterations k=0 of initial coefficients.ε=1 in the present embodiment.K is assigned to by 1.
Step 3: obtaining QMFB lowpass analysis filter H under kth time iteration using the solution of IGS technical optimization0(w) filter
Wave device coefficientConcrete operations are as follows:
3-1. according to(coefficient that iteration initial coefficients or preceding an iteration obtain) calculates obtained by -1 iteration of kth
The reconstructed error of QMFBAs shown in formula (2).
In formula (2),Indicate the amplitude response of lowpass analysis filter in QMFB；It indicates
The amplitude response of high pass analysis filter in QMFB；" " representing matrix dot product, the i.e. corresponding element of array are multiplied.
3-2. is defined shown in a series of constant arrays such as formula (3).
3-3. calculates the resulting QMFB reconstructed error of -1 iteration of kth by formula (4)About coefficientOne
Rank partial derivative
For 3-4. according to first order Taylor approximation, we obtain the reconstructed error of QMFB when kth time iteration
In formula (5),Represent QMFB lowpass analysis filter H when kth time iteration0(w) coefficient increment, the value are wait ask
Value, is specifically acquired in step 3-5.
We are just the reconstructed error e of QMFB in this wayr(h0) by being originally about coefficient h0Quadratic function equivalence at closing
In filter coefficient incrementLinear function.
At this time when kth time iteration QMFB stopband attenuationIt is expressed as about incrementLinear function such as formula (6) institute
Show.
3-5. determines filter coefficient increment according to one of following nine kinds of methodsSize.
Method one: being solved according to the convex optimization problem that formula (7) are expressed, and determines the coefficient increment of kth time iteration
In formula (7), | | | |∞Indicate Infinite Norm operation, | | | |2Indicate 2 norm operations.δ needs minimize
Intermediate variable；σ indicates the stopband maximum attenuation desired value being manually set, and α is weight coefficient.
This method can be stated are as follows: in the case where meeting formula (7c) and (7d) at the same time, the levoform in formula (7b) be allowed to reach
It minimizesAs kth time iterationIt, can be easily by the tool box CVX of matlab software in practical operation
Find out QMFB lowpass analysis filter H when kth time iteration0(w) coefficient increment
This method select Johnston method in " weighted sum of reconstructed error energy and stopband energy " this about prototype
The biquadratic function of filter coefficient designs QMFB as objective function, with our optimization method can it is of equal value at about's
The l of linear function2Norm minimum problem.
Method two: the formula (7b) in method one is replaced with formula (7e), and determines the coefficient increment of kth time iteration
This method is by the l of reconstructed error2The l of norm and stopband attenuation2The weighted sum of norm is as objective function.The minimum
The objective function of change can be understood as be reconstructed error energy root side and stopband attenuation energy root side weighted sum, with
This objective function is different reconstructed error energy with the weighted sum of stopband energy in Johnston method, and identical is reconstruct
Error and stopband attenuation are all based on criterion of least squares.
Method three: the formula (7b) in method one is replaced with formula (7f), and determines the coefficient increment of kth time iteration
This method is by the l of the Infinite Norm of reconstructed error and stopband attenuation2The weighted sum of norm is as objective function.This is most
The objective function of smallization can be understood as be maximum reconstructed error and stopband attenuation energy root side weighted sum, reconstructed error it is excellent
Change and is based on least most rule, and stopband attenuation is based on criterion of least squares.
Method four: the formula (7b) in method one is replaced with formula (7g), and determines the coefficient increment of kth time iteration
This method is using the weighted sum of the Infinite Norm of reconstructed error and the Infinite Norm of stopband attenuation as objective function.It should
The objective function of minimum can be understood as be maximum reconstructed error and stopband maximum attenuation weighted sum, the optimization of reconstructed error
Based on least most rule, stopband attenuation is also based on least most rule.
Method five: the formula (7b) in method one is replaced with formula (7h), and determines the coefficient increment of kth time iteration
This method directly minimizes maximum reconstructed error under stopband maximum attenuation constraint condition.The optimization of reconstructed error
Based on least most rule, stopband attenuation is also based on least most rule.
Method six: formula (7c) this constraint condition in minimizing technology one determines the coefficient increment of kth time iteration
Method seven: formula (7c) this constraint condition in minimizing technology two determines the coefficient increment of kth time iteration
Method eight: formula (7c) this constraint condition in minimizing technology three determines the coefficient increment of kth time iteration
Method nine: formula (7c) this constraint condition in minimizing technology four determines the coefficient increment of kth time iteration
In method one, two, six, seven, nine, the value of weight coefficient α is 1；In method three, the value of weight coefficient α is
0.1；In method four, the value of weight coefficient α is 0.01；In method eight, the value of weight coefficient α is 0.5.
3-6. calculates kth time iterative filter coefficient
Step 4: k is increased 1, and repeat step 3 if formula (8) is invalid.It, will if formula (8) is set upMake
The QMFB lowpass analysis filter H gone out for final design0(w) coefficient.In same secondary design, step 3 determines coefficient increment
Using the same method.
In formula (8), δkIt is δ (the i.e. minimum of kth time iteration Chinese style (7b) levoform that the formula (7) in kth time iteration determines
Value).δk-1It is the δ that the formula (7) in -1 iteration of kth determines.
For effectiveness of the invention, computer simulation emulation has been carried out to the present invention.
Design requirement in analog simulation: ptototype filter order N is equal to 32, and the frequency points L on Whole frequency band is 8N, resistance
Band cutoff frequency fs is 0.6 π, minimizes reconstructed error, maximizes stopband attenuation.
Determine that the iteration step length ε in step 2 is to take 1, iteration ends coefficient ε1It is 10-3, ptototype filter iteration is initially
NumberMethod one is used in step 3, weighted value α value is 1, and stopband is most
Big decaying preset value σ is set as 10(-36.43/20)。
By 5 iteration, final QMFB lowpass analysis filter H is obtained0(w) filter coefficient is as shown in table 1 (only
List symmetrical half coefficient), corresponding QMFB amplitude-frequency response and reconstructed error frequency response are as shown in Figures 2 and 3.
1 QMFB lowpass analysis filter H of table0(w) coefficient table
Finally with the filter coefficient obtained, the reconstructed error peak value PRE (peak of QMFB is calculated
Reconstruction error), the decaying AS (stopband edge attenuation) of stopband cutoff frequency point and resistance
Band peak-ripple PSR (peak stopband ripple).Calculation formula is as follows:
PRE=max | 20log10(|H0(w)|2+|H0(w+π)|2)|}
AS=-20log10|H0(ws)|
PSR=-max { 20log10|H0(wl) |, wl∈[ws,...,wL]
Wherein, | H0(w) | it is the amplitude response of gained lowpass analysis filter；For gained high pass analysis
The amplitude response of filter, | H0(ws) | for the amplitude response on gained lowpass analysis filter stop bend cutoff frequency point；Work as wl∈
[ws,...,wL] when, | H0(wl) | for the amplitude response in gained lowpass analysis filter stop bend.The index being calculated such as table 2
It is shown
According to above-mentioned verifying analog simulation method, analog simulation is successively re-started using method two to nine in step 3.
Weighted value α is 1 in method two, and stopband maximum attenuation preset value σ is set as 10(-36.43/20)；Weighted value α in method three
It is 0.1, stopband maximum attenuation preset value σ is set as 10(-36.34/20)；Weighted value α is 0.01 in method four, and stopband maximum attenuation is pre-
If value σ is set as 10(-36.34/20)；Stopband maximum attenuation preset value σ is set as 10 in method five(-36.34/20)；It is weighted in method six
Value α is 1；Weighted value α is 1 in method seven；Weighted value α is 0.5 in method eight；Weighted value α is 1 in method nine.
The resulting QMFB of the present invention and the resulting QMFB index comparison of conventional design method are as shown in table 2.Method three is obtained
The QMFB lowpass analysis filter H obtained0(w) the corresponding amplitude-frequency response of filter coefficient and reconstructed error frequency response such as Fig. 4
With shown in Fig. 5.The QMFB lowpass analysis filter H obtained of method four0(w) the corresponding amplitude-frequency response of filter coefficient and again
The response of structure error frequency is as shown in Figure 6 and Figure 7.
2 present invention of table is compared with conventional method key index
From table 2 it can be seen that present invention QMFB obtained is substantially better than other sides on above-mentioned every key index
Method.
Claims (5)
1. the two channel quadrature mirror filter group design methods based on iterative gradient search, it is characterised in that: Step 1: according to
Design requirement determines frequency points L, the order N of linear phase ptototype filter, stopband cutoff frequency fs on Whole frequency band:
Low-pass filter full rate matrix U is determined respectively by formula (1a), (1b), (1c)t, stop-band frequency matrix UsIt is filtered with high pass
Wave device full rate matrix UT, (w+ π)；
Ut=[c (w1) ..., c (ws) ..., c (wL)]T (1a)
Us=[c (ws), c (ws+1) ..., c (wL)]T (1b)
UT, (w+ π)=[c (w1+ π) ..., c (ws+ π) ..., c (wL+π)]T (1c)
In formula (1), wsIndicate stopband cutoff frequency point；
Step 2: setting iteration step length ε, iteration ends coefficient ε1, ptototype filter iteration initial coefficientsK is assigned to by 1；
QMFB lowpass analysis filter H under kth time iteration is obtained Step 3: solving0(w) filter coefficient
3-1. calculates the reconstructed error of QMFB obtained by -1 iteration of kthAs shown in formula (2)；
In formula (2), " " representing matrix dot product；
3-2. is defined shown in a series of constant arrays such as formula (3)；
h1=[h1,0, h1,1..., h1, N/2-1]T=[1,0 ..., 0,0]T
h2=[h2,0, h2,1..., h2, N/2-1]T=[0,1 ..., 0,0]T
hn=[hN, 0, hN, 1..., hN, N/2-1]T=[0,0 ..., 0,1]T, n=N/2 (3)
3-3. calculates the resulting QMFB reconstructed error of -1 iteration of kthAbout coefficientFirst-order partial derivative
As shown in formula (4)；
The reconstructed error of QMFB when 3-4. calculates kth time iterationAs shown in formula (5)；
In formula (5),Represent QMFB lowpass analysis filter H when kth time iteration0(w) coefficient increment；
The stopband attenuation of QMFB when kth time iterationAs shown in formula (6)；
3-5. determines filter coefficient increment according to one of following nine kinds of methodsSize；
Method one: being solved according to the convex optimization problem that formula (7) are expressed, and determines the coefficient increment of kth time iteration
In formula (7), | | | |∞Indicate Infinite Norm operation, | | | |2Indicate 2 norm operations；δ is the intermediate change for needing to minimize
Amount；σ indicates stopband maximum attenuation desired value, and α is weight coefficient；
Method two: the formula (7b) in method one is replaced with formula (7e), and determines the coefficient increment of kth time iteration
Method three: the formula (7b) in method one is replaced with formula (7f), and determines the coefficient increment of kth time iteration
Method four: the formula (7b) in method one is replaced with formula (7g), and determines the coefficient increment of kth time iteration
Method five: the formula (7b) in method one is replaced with formula (7h), and determines the coefficient increment of kth time iteration
Method six: formula (7c) this constraint condition in minimizing technology one determines the coefficient increment of kth time iteration
Method seven: formula (7c) this constraint condition in minimizing technology two determines the coefficient increment of kth time iteration
Method eight: formula (7c) this constraint condition in minimizing technology three determines the coefficient increment of kth time iteration
Method nine: formula (7c) this constraint condition in minimizing technology four determines the coefficient increment of kth time iteration
3-6. calculates kth time iterative filter coefficient
Step 4: k is increased 1, and repeat step 3 if formula (8) is invalid；It, will if formula (8) is set upAs most
The QMFB lowpass analysis filter H designed eventually0(w) coefficient；In same secondary design, step 3 determines that coefficient increment uses
The same method；
In formula (8), δkIt is the δ that the formula (7) in kth time iteration determines；δk-1It is the δ that the formula (7) in -1 iteration of kth determines.
2. the two channel quadrature mirror filter group design methods according to claim 1 based on iterative gradient search,
It is characterized in that: in step 2, ptototype filter iteration initial coefficientsValue is [0,0 ..., 0,0.5]TOr pass through Parks-
McClellan method or Direct Design Method obtain.
3. the two channel quadrature mirror filter group design methods according to claim 1 based on iterative gradient search,
It is characterized in that: in step 2, iteration step length ε=1.
4. the two channel quadrature mirror filter group design methods according to claim 1 based on iterative gradient search,
It is characterized in that: in step 2, iteration ends coefficient ε1=10-3。
5. the two channel quadrature mirror filter group design methods according to claim 1 based on iterative gradient search,
Be characterized in that: in the method one, two, six, seven, nine of step 3-5, the value of weight coefficient α is 1；In method three, weight coefficient α
Value be 0.1；In method four, the value of weight coefficient α is 0.01；In method eight, the value of weight coefficient α is 0.5.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20040136448A1 (en) * | 1993-03-17 | 2004-07-15 | Miller William J. | Method and apparatus for signal transmission and reception |
| CN1976226A (en) * | 2006-12-20 | 2007-06-06 | 北京中星微电子有限公司 | Orthogonal filter set designing method and apparatus |
| CN107256537A (en) * | 2017-06-06 | 2017-10-17 | 桂林电子科技大学 | A kind of design method for designing two passage orthogonal graph wave filter groups |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US20040136448A1 (en) * | 1993-03-17 | 2004-07-15 | Miller William J. | Method and apparatus for signal transmission and reception |
| CN1976226A (en) * | 2006-12-20 | 2007-06-06 | 北京中星微电子有限公司 | Orthogonal filter set designing method and apparatus |
| CN107256537A (en) * | 2017-06-06 | 2017-10-17 | 桂林电子科技大学 | A kind of design method for designing two passage orthogonal graph wave filter groups |
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| CN111010144A (en) * | 2019-11-25 | 2020-04-14 | 杭州电子科技大学 | Improved two-channel IIR QMFB design method |
| CN111010144B (en) * | 2019-11-25 | 2020-09-15 | 杭州电子科技大学 | Improved two-channel IIR QMFB design method |
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