CN105656452B - A kind of design method of tone filter - Google Patents

A kind of design method of tone filter Download PDF

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Publication number
CN105656452B
CN105656452B CN201511019198.9A CN201511019198A CN105656452B CN 105656452 B CN105656452 B CN 105656452B CN 201511019198 A CN201511019198 A CN 201511019198A CN 105656452 B CN105656452 B CN 105656452B
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China
Prior art keywords
filter
design
optimization problem
value
optimal solution
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CN201511019198.9A
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Chinese (zh)
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CN105656452A (en
Inventor
凌永权
张小志
李志光
方百立
梁卓銘
黄永恆
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Guangdong University of Technology
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Guangdong University of Technology
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H21/00—Adaptive networks
    • H03H21/0012—Digital adaptive filters
    • H03H21/0043—Adaptive algorithms

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  • Soundproofing, Sound Blocking, And Sound Damping (AREA)
  • Piezo-Electric Or Mechanical Vibrators, Or Delay Or Filter Circuits (AREA)

Abstract

The invention discloses a kind of design methods of tone filter, including：S1, initialization iterations k=0 andValue, set one permission error amountS2, as k >=0, design optimization problemS3 finds optimization problemOptimal solutionDesign the amplitude and phase of filter；S4, design optimization problemS5 finds optimization problemOptimal solutionDesign exponent number, decay factor and the frequency of filter.The present invention greatly reduces the calculation amount of problem solving, and a kind of optimization method of highly effective is provided for filter design.

Description

A kind of design method of tone filter
Technical field
The present invention relates to tone filter design field, the design method of specifically a kind of tone filter.
Background technology
Continuous time filter has the characteristics such as high working frequency, broadband, big dynamic range and stability, answers extensively For fields such as tip Medical Devices, communication and Audio Signal Processings.Continuous time unreasonable wavenumber filter is that continuous time is reasonable The popularization of wavenumber filter has better frequency selective characteristic.But since continuous time unreasonable wavenumber filter is non-linear phase Position, design is challenging, and includes fractional order differential in the frequency response of continuous time unreasonable wavenumber filter, sets Meter is to solve for a non-convex optimization problem of Non-smooth surface, needs largely to calculate to seek optimal solution in practical applications.
Invention content
The present invention proposes a kind of audio for non-convex smooth perturbation problem required in the design of irrational number continuous time filter The design method of filter.
In order to solve the above technical problems, the present invention is achieved by the following scheme：
The frequency response of a kind of design method of tone filter, the tone filter is H (ω)：
The design method includes：
S1, initialization iterations k=0 andValue, set one permission error amount
S2, as k >=0, design optimization problem
S3 finds optimization problemOptimal solutionDesign the amplitude and phase of filter；
S4, design optimization problem
Wherein, ε represents the permitted passband of filter and the maximum ripple value of suppressed frequency band；
S5 finds optimization problemOptimal solutionExponent number, decay factor and the frequency of filter are designed, and is increased Add the value of k, return to step S1.
Further, the step S5 includes：
S501, initiation parameter：δ1＞ 0, δ2＞ 0, σ ∈ (0,1), α ∈ (0,1),C=0, k >=0, penalty parameter βk,-1＞ 0, symmetric positive definite matrix Qk,0；
S502 designs subproblemOptimal descent direction is sought in c >=0
Wherein,It is optimization problemSolution, ifAlgorithm terminates；Otherwise, S503 is entered step；
S503, design value function seek optimal step size tk；
For k >=0, c >=0, defined nucleotide sequence { 1, σ, σ2... } and in first value be tk：
If
If
S504 calculates Qk,c+1,Increase c values, returns and continue return to step S502；
S505 works as satisfactionWhen condition, algorithmic statement is terminated and is calculated, and is obtained entirely optimizing and be asked Inscribe the optimal solution of (P)To design filter；Otherwise, return to step S502 continues to calculate, until algorithmic statement Until.
The present invention greatly reduces the calculation amount of problem solving, and a kind of optimization calculation of highly effective is provided for filter design Method.
Description of the drawings
Fig. 1 is the frequency response chart of the tone filter of the present invention.
Fig. 2 is the spectrogram of original aircraft noise signal；
Fig. 3 is the filtered spectrogram of aircraft noise signal to Fig. 2 using Butterworth filters；
Fig. 4 is aircraft noise signal filtered spectrogram of the tone filter using the present invention to Fig. 2.
Specific implementation mode
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete Site preparation describes, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on Embodiment in the present invention, those of ordinary skill in the art are obtained every other without creative efforts Embodiment shall fall within the protection scope of the present invention.
The present invention provides a kind of design method of tone filter, and the frequency response of the tone filter is
As shown in Figure 1, it is a kind of design method of design method of tone filter of the present invention includes：
S1, initialization iterations k=0 andValue, set one permission error amount
S2, as k >=0, design optimization problem
S3 finds optimization problemOptimal solutionDesign the amplitude and phase of filter；
S4, design optimization problem
Wherein, ε represents the permitted passband of filter and the maximum ripple value of suppressed frequency band；
S5 finds optimization problemOptimal solutionExponent number, decay factor and the frequency of filter are designed, and is increased Add the value of k, return to step S1.
It is that a solution is non-above due to including fractional order differential in the frequency response of irrational number continuous time filter Smooth non-convex problem.In this regard, the present invention proposes to be approximately first smooth non-convex target letter the non-convex object function of Non-smooth surface Number recycles Norm Relaxed SQP methods to seek its optimal solution.The step S5 includes：
S501, initiation parameter：δ1＞ 0, δ2＞ 0, σ ∈ (0,1), α ∈ (0,1),C=0, k >=0, penalty parameter βk,-1＞ 0, symmetric positive definite matrix Qk,0；
S502 designs subproblemOptimal descent direction is sought in c >=0
Wherein,It is optimization problemSolution, ifAlgorithm terminates；Otherwise, S503 is entered step；
S503, design value function seek optimal step size tk；
For k >=0, c >=0, defined nucleotide sequence { 1, σ, σ2... } and in first value be tk：
If
If
S504 calculates Qk,c+1,Increase c values, returns and continue return to step S502；
S505 works as satisfactionWhen condition, algorithmic statement is terminated and is calculated, and is obtained entirely optimizing and be asked Inscribe the optimal solution of (P)To design filter；Otherwise, return to step S502 continues to calculate, until algorithmic statement Until.
The present invention greatly reduces the calculation amount of problem solving, and a kind of optimization calculation of highly effective is provided for filter design Method.
A tone filter is designed by the design method, the tone filter is by N number of fractional order Gammatone Filter is constituted；The shock response of the tone filter is h (t),hi(t) it is i-th of Gammatone The shock response of filter,Wherein, Ai,mi,bi, fiAnd φiIt indicates respectively Amplitude, exponent number, decay factor, frequency and the phase of i-th of Gammatone filter impulse response, u (t) represent jump function； miFor score.
As shown in Figure 1, it is the frequency response chart of the tone filter of the present invention.
Please comparison diagram 2, Fig. 3 and Fig. 4, Fig. 2 is the spectrogram of original aircraft noise signal, and Fig. 3 is to use Butterworth For filter to the filtered spectrogram of aircraft noise signal of Fig. 2, Fig. 4 is that tone filter using the present invention flies Fig. 2 The filtered spectrogram of machine noise signal.
As it can be seen that after tone filter using the present invention is to noise filtering, filter effect is more preferable.
The shock response of the tone filter of the present invention is made of polynomial function, exponential function, cosine function, and response exists It is more concentrated in time-frequency domain, frequency selectivity is good；The response of this filter impulse is index decreased, meets absolutely integrable item Part has stability；Parameter in the response of this filter impulse, Ai,mi,bi, fiAnd φiThere can be spirit with optimization design respectively Activity.Better audio defeat effect may be implemented in the tone filter of the present invention.
One of ordinary skill in the art will appreciate that realizing all or part of flow in above-described embodiment method, being can be with Relevant hardware is instructed to complete by computer program, the program can be stored in a computer read/write memory medium In, the program is when being executed, it may include such as the flow of the embodiment of above-mentioned each method.Wherein, the storage medium can be magnetic Dish, CD, read-only memory (Read-Only Memory, ROM) or random access memory (Random Access Memory, RAM) etc..
The above is the preferred embodiment of the present invention, it is noted that for those skilled in the art For, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also considered as Protection scope of the present invention.

Claims (1)

1. a kind of design method of tone filter, which is characterized in that the frequency response of the tone filter is H (ω)：
The design method includes：
S1, initialization iterations k=0 andValue, set one permission error amount
S2, as k >=0, design optimization problem
S3 finds optimization problemOptimal solutionDesign the amplitude and phase of filter；
S4, design optimization problem
Wherein, ε represents the permitted passband of filter and the maximum ripple value of suppressed frequency band；
S5 finds optimization problemOptimal solutionExponent number, decay factor and the frequency of filter are designed, and increases k Value, return to step S1；
The step S5 includes：
S501, initiation parameter：δ1>0, δ2>0, σ ∈ (0,1), α ∈ (0,1),C=0, k >=0, penalty parameter βk,-1>0, it is right Claim positive definite matrix Qk,0；
S502 designs subproblemOptimal descent direction is sought in c >=0
Wherein,It is optimization problemSolution, ifAlgorithm terminates；Otherwise, S503 is entered step；
S503, design value function seek optimal step size tk；
For k >=0, c >=0, defined nucleotide sequence { 1, σ, σ2... } and in first value be tk：
If
If
S504 calculates Qk,c+1,Increase c values, returns and continue return to step S502；
S505 works as satisfactionWhen condition, algorithmic statement terminates and calculates, obtains entire optimization problem (P) Optimal solutionTo design filter；Otherwise, return to step S502 continues to calculate, until algorithmic statement.
CN201511019198.9A 2015-12-28 2015-12-28 A kind of design method of tone filter Expired - Fee Related CN105656452B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201511019198.9A CN105656452B (en) 2015-12-28 2015-12-28 A kind of design method of tone filter

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Application Number Priority Date Filing Date Title
CN201511019198.9A CN105656452B (en) 2015-12-28 2015-12-28 A kind of design method of tone filter

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CN105656452A CN105656452A (en) 2016-06-08
CN105656452B true CN105656452B (en) 2018-09-25

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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101415660A (en) * 2006-03-31 2009-04-22 住友化学株式会社 Process for producing tertiary olefin and aliphatic alcohol

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140310326A1 (en) * 2013-04-10 2014-10-16 King Fahd University Of Petroleum And Minerals Adaptive filter for system identification

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101415660A (en) * 2006-03-31 2009-04-22 住友化学株式会社 Process for producing tertiary olefin and aliphatic alcohol

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
"Auditory-motivated Gammatone wavelet transform";Arun Venkitaraman等;《Signal Processing》;20140131;第94卷;第608-619页 *
"Practical Gammatone-Like Filters for Auditory Processing";AG Katsiamis等;《EURASIP Journal on Audio, Speech, and Music Processing》;20071231;第1-15页 *
"基于 Gammatone滤波器组的听觉特征提取";胡峰松等;《计算机工程》;20121130;第38卷(第21期);第168-174页 *

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