CN110086452A - A kind of design method of the sparse FIR notch filter of low complex degree - Google Patents
A kind of design method of the sparse FIR notch filter of low complex degree Download PDFInfo
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- CN110086452A CN110086452A CN201811508545.8A CN201811508545A CN110086452A CN 110086452 A CN110086452 A CN 110086452A CN 201811508545 A CN201811508545 A CN 201811508545A CN 110086452 A CN110086452 A CN 110086452A
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
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- H03H17/02—Frequency selective networks
- H03H17/06—Non-recursive filters
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- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H2017/0072—Theoretical filter design
- H03H2017/0081—Theoretical filter design of FIR filters
Abstract
The invention discloses a kind of small ripple of realization, the design method of the linear phase fir notch filter of low tap number and low complex degree.This method maximizes the common minor in shared MCM module on the basis of SPT coding method, based on common minor technology for eliminating, recombines filter coefficient set according to the level of sensitivity of minor, the quantity of adder is further decreased.The sparse FIR notch filter that the present invention that simulation result shows designs under the requirement of same design index, the number of adders of the linear phase fir notch filter that the present invention realizes is fewer by 51% or more than the number of adders of domestic and international existing similar filter.
Description
Technical field
The invention belongs to digital signal processing technique fields, provide a kind of sparse, efficient, low complex degree linear phase
The design method of FIR (finite impulse response (FIR)) notch filter.
Background technique
Notch filter can effectively filter out the frequency content interference of specific extremely narrow frequency range, and to the letter except the frequency range
Number carry out high efficiency of transmission, it is very widely used in fields such as the communication technology, bioengineering, Radar Sonar, measuring instruments.In number
In word signal processing, digital filtering technique is its important component part, and from impulse response angle digital signal filter
Device generally can be divided into finite impulse response (FIR) (FIR) filter and (infinite impulse response) iir filter.And from frequency response angle
It can be divided into following several: low-pass filter, high-pass filter, bandpass filter, bandstop filter, notch filter.Trap filter
Wave device is for eliminating certain specific frequencies in input signal and being relatively free of influence to residual frequency.Signal processing, communication and
The fields such as biomedical engineering are widely used.Sparse linear phase fir (finite impulse response (FIR)) notch filter is coefficient
Notch filter with sparse characteristic (number of non-zero tap coefficient is less than filter order).Its realization of sparse filter
Addition and number of multipliers used far fewer than with the comparable similar filter of its filter effect, therefore, sparse filtering utensil
There are arithmetic speed height, arithmetic eror small and low power consumption and other advantages.
The method of the reduction FIR filter hardware realization complexity proposed at present is broadly divided into two major classes.A kind of method is
FIR filter is designed using Corresponding Sparse Algorithm, under the premise of meeting filter frequency domain design requirement, the time domain of filter is enabled to rush
Swashing response has zero-valued taps coefficients more as far as possible, achieves adder number of multipliers used and greatly reduces.Second class
The method that hardware realization complexity is effectively reduced is the FIR filter optimization design based on Multiple Constant Multiplication (MCM) technology.And it is right
In the design method of the notch filter proposed, the design method of CHEN.Jiajia and CHANG.C can be classical at last,
On the basis of SPT coding method, the common minor in shared MCM module is maximized based on common minor technology for eliminating, into one
Step reduces the quantity of adder.
Summary of the invention
Object of the present invention is to design to realize small ripple, the notch filter of low tap number, and provide a kind of completely new design
Method --- can design it is sparse, efficiently, the method for the linear phase fir notch filter of low complex degree.
Specific step is as follows for the design method of the sparse FIR notch filter of low complex degree provided by the invention:
1st, the FIR trap for obtaining meeting the requirement of frequency domain performance design using sparse FIR notch filter algorithm for design is former
Beginning filter coefficient；
2nd, convert mathematical optimization problem for the design problem of sparse FIR notch filter, using IROMP algorithm into
Row solves to obtain FIR trap original filter coefficient；
3rd, CSD coding is carried out to FIR trap original filter coefficient；
4th, the sensitivity function for introducing 2 minor sensitivity and orphan successively selects rationally according to the size of sensitivity
2 minors or orphan recombine filter coefficient set.
(below by taking I Linear phase FIR filter as an example, equally applicable and other II of the invention, III, IV Linear phase
Position FIR filter):
(1) initial parameter is constructed according to design requirement:
The present invention is required according to design parameter, including trap frequency setNotch depth d (dB), notch bandwidth
Δ ω, pass band damping α (dB) (or passband ripple δ), pass band damping α and passband ripple δ can be mutually converted, the relationship of the two are as follows:
Give above-mentioned design objective, the frequency response H (e of FIR notch filterjω) should meet:
Wherein
(2) the FIR trap original filter for meeting the requirement of frequency domain performance design is obtained using sparse filter algorithm for design
Coefficient h (n), 0≤n≤N, it is assumed that notch filter is I Linear phase FIR filter, i.e. order N is even number, and h (n) is real
It counts and there is even symmetry, then the frequency response H (e of FIR notch filterjω) meet H (ejω)=e-jMωH0(ω), wherein M=
N/2, H0(ω) is zero phase response, can be indicated are as follows:
Then convert the design problem of sparse FIR notch filter to following mathematical optimization problem:
min||h||0 (4a)
S.t. | c (ω) h-1 | < δ, ω ∈ [0, π]-Ω0 (4b)
Formula (4) is to l0Objective function under norm is solved, this optimization problem is that a complicated NP-hard is asked
Topic is solved the problems present invention to formula (4) using IROMP algorithm, obtains the filter coefficient vector h of rarefaction
=[h (0) h (1) ... h (N)]T；
(3) assume that number of encoding bits are B, CSD coding is carried out to each coefficient in FIR filter original coefficient vector h.
If the CSD coded representation of n coefficient h (n) isThen h (n) and hq(n) there is following turn
Change relationship:
Wherein [] indicates the operation that rounds up；Determine quantization word length B, to sparse FIR notch filter coefficient vector h into
Row CSD coding, if the CSD coded representation of n coefficient h (n) isThen h (n) and hq(n)
Transforming relationship is as follows
Wherein [] indicates the operation that rounds up, and then obtains the binary coding coefficient matrix of N × B:
In coefficientIn, ifWithFor non-zero bit, thenIt is (intermediate
There are j 0) corresponding multinomials to be known as 2 minors of j rank, if the nonzero digit of 2 minor head and the tail positions of j rankWithTogether
Number, referred to as even 2 minors of j rank, such as 101,If contrary sign, referred to as odd 2 minors of j rank, such asIf certain
When any type of 2 minors can not be constituted by containing only an independent nonzero digit in one quantization parameter, such as { 00100000 },
It is known as orphan, if being known as common minor there are 2 minors of identical order between coefficient inside or coefficient.Input
After 2 minors of signal and some j rank carry out a multiplication operation, other positions can with the minor of identical order j with the minor
Directly with this as a result, adder quantity can be reduced by CSE technology here it is the basic principle of CSE technology.For example, false
If 12 quantization word length coefficientsIf being directly realized by coefficient hq(1), as shown in Fig. 2 (a), 5 are needed
A adder, if to hq(1) all 1 rank, 2 minors 101 carry out CSE in, and as shown in Fig. 2 (b), adder number is reduced to
3；CSE technology can also be applied between different coefficients, ifAs shown in figure 3, by all total
It extracts with 2 minors 101, and is directly realized by coefficient hq(1) and hq(2) it compares, adder quantity is reduced to 6 from 11.
To count hqIn the position that occurs of all 2 minors of j rank, introduce the location matrix CSP of B-2 N × B(j), j=1,
2 ... B-2, CSP(j)It is labelled with hqIn it is all have form bi 0 … 0bi-j-12 minors of j rank of (centre has j 0) occur
Position, in matrix element value be 0,1 orIf CSP(j)(n, i)=1 orThen indicate hq(n) inWithConstitute j
Even (surprise) 2 minors of rank, if CSP(j)(n, i)=0, then it represents that in hq(n) 2 sons of any j rank are not present on corresponding position
Formula, we withWithFor, N=2, B=12, h at this timeq
Corresponding 1 rank, 2 ranks, 9 ranks and 10 ranks, 2 minor location matrixs are as follows:
To count hqIn the position that occurs of all orphans, introduce the location matrix CSP of a N × B(0)If CSP(0)(n, i)
=1 orIndicate n-th of quantization parameter hq(n) in i-th bit there are independent nonzero digit 1 or
(4) under the design parameter of given notch filter, by reasonably selecting 2 minors or orphan to carry out weight
Structure can quickly obtain desired coefficient set, for this purpose, invention introduces the sensitivity function of 2 minors of orphan and j rank,
It enablesIt is expressed as coefficient set hqOrphan in middle n coefficient, ith bit position,J=1,2 ... B-2 represent hq(n) in
'sWith2 minors of j rank of composition, then sensitivity functionIt is expressed as
Wherein L is sampling number, Hq(ω) is quantization parameter collection hqCorresponding filter freguency response,Being will
2 minors of j rank or orphan are from coefficient set hqCorresponding frequency response after middle removal, sensitivity function represent 2 minors of a j rankOr orphanFrequency response error caused by removal.
According to formula (8) design factor collection hqIn each j rank 2 minors and orphan sensitivity, corresponding result is put into B-1
The sensitivity matrix SEN of N × B(j), in j=0,1 ... B-2, enable hrThe reconstruction coefficients matrix for indicating N × B dimension, is initialized as
Full 0 matrix according to the size of sensitivity, will successively select 2 minors of reasonable j rank or orphan to copy in each iteration
Reconstruction coefficients matrix hrIn, until hrCorresponding filter passband ripple δrWith notch depth drIt meets the requirements.
The invention has the following beneficial effects:
1, it is sunken to provide a kind of sparse, efficient, low complex degree linear phase fir (finite impulse response (FIR)) for the first time by the present invention
The design method of wave filter.
2, the present invention can design the linear phase fir notch filter of low non-zero tap number, and the sparsity of filter can make
It realizes that adder number of multipliers used greatly reduces, so as to improve its arithmetic speed, reduce arithmetic eror and hardware
Implementation complexity, and then save hardware resource.
3, simulation result shows under the requirement of same design index, the linear phase fir notch filter that the present invention realizes
The number of adders of device is fewer by 51% or more than the number of adders of domestic and international existing similar filter.
Detailed description of the invention
Fig. 1 is inventive algorithm flow chart；
Fig. 2 is the frequency response chart for realizing design gained FIR notch filter；
The frequency response chart for the notch filter that Fig. 3 is obtained according to the present invention.
Specific embodiment
Embodiment 1:
Specific step is as follows for the design method of the sparse FIR notch filter of low complex degree provided by the invention:
1st, the FIR trap for obtaining meeting the requirement of frequency domain performance design using sparse FIR notch filter algorithm for design is former
Beginning filter coefficient；
2nd, convert mathematical optimization problem for the design problem of sparse FIR notch filter, using IROMP algorithm into
Row solves to obtain FIR trap original filter coefficient；
3rd, CSD coding is carried out to FIR trap original filter coefficient；
4th, the sensitivity function for introducing 2 minor sensitivity and orphan successively selects rationally according to the size of sensitivity
2 minors or orphan recombine filter coefficient set.
In order to verify the validity of the filter design method, computer simulation emulation has been carried out to this method.
Design requirement: document: (CHEN Jiajia, TAN Jinghong, CHANG C, et α l.A new cost- is utilized
aware sensitivity-driven algorithm for the design of FIR filters[J].IEEE
Transactions on Circuits and Systems-I:Regular Papers, 2017,64 (6): 1588-1598.)
Given in go out FIR notch filter design parameter index, trap frequency point set { 0.1 π, 0.25 π, 0.76 π }, notch bandwidth
The π of Δ ω=0.061, passband ripple δ=- 0.95dB and notch depth d=-60dB, the present invention are designed sparse with IROMP algorithm
FIR notch filter, according to the calculating of weighted value, in the filter coefficient vector h for obtaining rarefaction, we are compiled using CSD
Code and common minor eliminate thought and iterate to calculate to obtain filter reconstruction coefficients matrix hr。
Step 1: it is required according to the design parameter of FIR notch filter, pass band damping α and passband ripple δ can mutually turn
Change, the relationship of the two are as follows:
The frequency response H of ideal FIR notch filterd(ejω) it is as follows:
Wherein
Step 2: the original filter of FIR trap for meeting the requirement of frequency domain performance design is obtained using sparse filter algorithm for design
Wave device coefficient h (n), 0≤n≤N, it is excellent that we will convert following mathematics for the design problem of sparse FIR notch filter
Change problem:
min ||h||0 (3a)
S.t. | c (ω) h-1 | < δ, ω ∈ [0, π]-Ω0 (3b)
The present invention solves above formula using IROMP algorithm, and the filter coefficient vector h=[h of rarefaction is calculated
(0) h(1) … h(N)]T；
Step 3: under conditions of determining quantization word length B=14,16 and 18, the filter to the rarefaction that step 2 solves
Each coefficient carries out CSD coding in wave device coefficient vector h, if the CSD coded representation of n coefficient h (n) isThen h (n) and hq(n) transforming relationship is as follows
Wherein [] indicates the operation that rounds up, and then obtains the binary coding coefficient matrix of N × B:
Step 4: by reasonably selecting 2 minors or orphan to be reconstructed, desired coefficient can quickly be obtained
Collection, invention introduces the sensitivity functions of 2 minors of orphan and j rank thus, enableIt is expressed as coefficient set hqIn n-th of system
Orphan on number, ith bit position,J=1,2 ... B-2 represent hq(n) inWith2 minors of j rank of composition,
Then sensitivity functionIt is expressed as
Wherein L is sampling number, Hq(ω) is quantization parameter collection hqCorresponding filter freguency response,It is
By 2 minors of j rank or orphan from coefficient set hqCorresponding frequency response after middle removal, sensitivity function represent 2 sons of a j rank
FormulaOr orphanFrequency response error caused by removal.
According to formula (6) design factor collection hqIn each j rank 2 minors and orphan sensitivity, corresponding result is put into B-1
The sensitivity matrix SEN of N × B(j), in j=0,1 ... B-2, enable hrThe reconstruction coefficients matrix for indicating N × B dimension, is initialized as
Full 0 matrix according to the size of sensitivity, will successively select 2 minors of reasonable j rank or orphan to copy in each iteration
Reconstruction coefficients matrix hrIn, until hrCorresponding filter passband ripple δrWith notch depth drIt meets the requirements, coefficient reconstructs process
It is as follows:
(1) sensitivity matrix SEN is utilized(j), j=0,1 ... B-2 find maximum 2 minors of sensitivity or orphan, and
By the nonzero digit of its corresponding bit position from hqCopy to hrIn, hqCorresponding position zero；
(2) judge hrCorresponding filter passband ripple δrWith notch depth drWhether meet the requirements.If satisfied, jumping to step
Rapid 5.If not satisfied, continuing in next step；
(3) if copying to h in step 1rIn bit be orphan, then continue step 4；If copying to h in step 1rIn ratio
Specially for 2 minors of k rank, then according to sensitivity from high to low gradually by 2 minors of corresponding k rank from hqCopy to hr, hqCorresponding position
Zero setting, until hrIt meets the requirements, jumps to step 5.If hqIn 2 minors of all k ranks be all copied to hrIn after, hrStill it is unsatisfactory for
It is required that then continuing step 4；
(4) coefficient set h is updatedqCorresponding location matrix CSP(j)With sensitivity matrix SEN(j), j=0,1 ... B-2 are jumped back to
Step 1；
(5) since 2 minors of k rank are copied to h in step 3rWhen can introduce the extremely low nonzero digit of several sensitivity,
So from hrThe middle nonzero digit for deleting these redundancies can further decrease adder quantity.H is calculated according to formula (7)rIt is all
The sensitivity of nonzero digit, in hrUnder the premise of meeting design requirement, from hrIn successively remove least sensitive nonzero digit.
It has been given in Table 1 respectively under conditions of quantifying word length B=14,16 and 18, through the invention in document two
The number (#NZ) of nonzero digit in coefficient set after the order of the filter that kind of algorithm designs, nonzero coefficient number, reconstruct
With adder number needed for realization.
Table 1
Claims (1)
1. a kind of design method of the sparse FIR notch filter of low complex degree, it is characterised in that this method can design low non-
The notch filter of zero tap number achieves adder number of multipliers used and reduces, so as to improve its arithmetic speed,
Reduce arithmetic eror and reduce energy consumption, the specific steps of this method include:
1st, it is required according to design parameter, including trap frequency setNotch depth d (dB), notch bandwidth Δ ω, lead to
Band attenuation alpha (dB) (or passband ripple δ), determines the correlation of pass band damping α and passband ripple δ, the frequency of FIR notch filter
Rate responds H (ejω) should meet:
Wherein
2nd, the FIR trap original filter coefficient for meeting the requirement of frequency domain performance design is obtained using sparse filter algorithm for design
H (n), 0≤n≤N convert the design problem of sparse FIR notch filter to following mathematical optimization problem:
min ||h||0 (4a)
S.t. | c (ω) h-1 | < δ, ω ∈ [0, π]-Ω0 (4b)
The present invention solves above formula using IROMP algorithm, obtains filter coefficient vector h=[h (0) h (1) of rarefaction
… h(N)]T；
3rd, determine quantization word length B, CSD coding carried out to sparse FIR notch filter coefficient vector h, obtain the two of N × B into
Code coefficient matrix processed:
To count hqIn the position that occurs of all 2 minors of j rank, introduce the location matrix CSP of B-2 N × B(j), j=1,2 ...
B-2, CSP(j)It is labelled with hqIn it is all have form bi0…0bi-j-1The position that 2 minors of j rank of (centre has j 0) occur,
In matrix element value be 0,1 orIf CSP(j)(n, i)=1 orThen indicate hq(n) inWithIt is even to constitute j rank
(surprise) 2 minors, if CSP(j)(n, i)=0, then it represents that in hq(n) 2 minors of any j rank are not present on corresponding position, are
Count hqIn the position that occurs of all orphans, introduce the location matrix CSP of a N × B(0)If CSP(0)(n, i)=1 orTable
Show n-th of quantization parameter hq(n) in i-th bit there are independent nonzero digit 1 or
It 4th,, can by reasonably selecting 2 minors or orphan to be reconstructed under the design parameter of given notch filter
Quickly to obtain desired coefficient set, for this purpose, being enabled invention introduces the sensitivity function of 2 minors of orphan and j rank
It is expressed as coefficient set hqOrphan in middle n coefficient, ith bit position,J=1,2 ... B-2 represent hq(n) inWith2 minors of j rank of composition, then sensitivity functionIt is expressed as
Wherein L is sampling number, Hq(ω) is quantization parameter collection hqCorresponding filter freguency response,It is by j rank 2
Minor or orphan are from coefficient set hqCorresponding frequency response after middle removal, sensitivity function represent 2 minors of a j rank
Or orphanFrequency response error caused by removal, according to formula (8) design factor collection hqIn 2 minors of each j rank and orphan
Sensitivity, corresponding result is put into the sensitivity matrix SEN of B-1 N × B(j), in j=0,1 ... B-2, enable hrIndicate N × B dimension
Reconstruction coefficients matrix, be initialized as full 0 matrix, in each iteration, by according to the size of sensitivity, successively selection is reasonable
2 minors of j rank or orphan copy to reconstruction coefficients matrix hrIn, until hrCorresponding filter passband ripple δrWith trap depth
Spend drIt meets the requirements.
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| WO2021046709A1 (en) * | 2019-09-10 | 2021-03-18 | 深圳市南方硅谷半导体有限公司 | Fir filter optimization method and device, and apparatus |
| CN116149600A (en) * | 2023-03-13 | 2023-05-23 | 深圳鸿芯微纳技术有限公司 | Method, device, equipment and medium for setting logic circuit of multi-constant multiplier |
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