CN103888104B - Method and system for designing FIR digital filter - Google Patents

Abstract

Provided are a method and system for designing an FIR digital filter. The method comprises the steps that modeling is carried out on the FIR digital filter according to a filter design need to obtain a mathematic model of the filter; the parameter limiting conditions of the filter are detailed according to the mathematic model to obtain a condition weighting model; the condition weighting model is solved through a genetic algorithm and a least square method to obtain an optimal filter coefficient; the FIR digital filter meeting actual filter needs is acquired according to the filter coefficient. According to the technical scheme, filter design with different properties can be obtained, the optimal filter design coefficient is obtained, and the optimal FIR digital filter is designed.

Description

Fir digital filter design method and system

Technical field

The present invention relates to digital filter design field, more particularly to a kind of fir digital filter design method and be System.

Background technology

In a wireless communication system, the receipt signal of terminal is typically mingled with noise and some useless signal components, needs Filtered by wave filter.For this reason, wave filter has very in modern signal processing and electrical application technology field Important using value.Traditional analog filter exist design complexity, huge structure, original paper quantity many shortcomings of.With meter Extensive application, the research and development of digital filter and application in wave filter design field for the calculation machine technology large scale integrated circuit technology Become main flow.Compared with analog filter, digital filter has high precision, and motility is good, the advantages of be easy to large-scale integrated, Current study hotspot focuses primarily upon the optimization design of digital filter.

Based on the actual performance of digital filter, digital filter is in signal processing, geologic prospect, digital communication, image There is very important effect in the fields such as transmission, Self Adaptive Control, and the optimization design of digital filter has very big practical significance.By In ideal filter, there is non-causality, for real time signal processing application, ideal filter is physically not can achieve , in actual design, designer typically can design to be had causal wave filter to approach ideal frequency response feature.

At present, design linear phase finite impulse response (FIR) (finite impulse response, fir) wave filter is main There are window function metht, Frequency Sampling Method, Chebyshev (chebyshev) approximatioss etc..Wherein window function metht is will using window function Ideal filter unit impact response unlimited in time is blocked the filter approximating ideal filter so that being designed Performance requirement.But window function metht design wave filter is very high for the types entail of window function and less efficient.Using frequency During rate method of sampling design fir wave filter, typically desired frequency response is divided at equal intervals frequency band.Simultaneously in order to slacken side Lobe, needs the frequency band of wave filter intermediate zone is optimized.Frequency Sampling Method is by up-sampling in frequency, and in sampled point On approach ideal filter frequency response with the method for interpolation.The design principle of Chebyshev approximation is by ideal frequency response Weighted approximation error and actual frequency response between is evenly dispersed into this passband and the stopband of wave filter, and minimizes The maximum error of wave filter.

Which kind of fir filter design method is all that ideal filter is approached.In order to more easily portray design With the approximation ratio of ideal filter, some scholars propose minimum mean-squared error criterion to the wave filter obtaining, the basis of this criterion Matter is so that the error energy of the filter freguency response and ideal filter frequency response actually obtaining is minimum.

With regard to based on mean square error minimize criterion the existing technical scheme of fir Optimal Design of Digital Filters just like Under:

Firstth, determine intermediate zone sample value by genetic algorithm, replace traditional look-up table, obtain at faster speed Optimize solution.Secondth, the design requirement according to expected frequency characteristic, sets up the Optimized model of window function weights, and by quick Self-adapted genetic algorithm carrys out solving-optimizing value.

Be directed to the first scheme above-mentioned, its be mainly characterized by original look-up table is replaced with genetic algorithm it is desirable to Obtained with speed faster and optimize solution.However, cannot ensure that trying to achieve solution is optimal solution using genetic algorithm, and algorithm implements tool There is certain complexity, the solution time is also longer so that it can not directly instruct engineering effort, the final solution obtaining is not It is exactly necessarily optimal solution, precision is low.And for second scheme, it is mainly characterized by and goes to solve window function using genetic algorithm Parameter, Study on Problems present in its filter design method substantially based on window function exists, including the choosing of window function Take, the Optimal Setting time length of parameter etc..

In sum, existing fir digital filter design techniques it is impossible to according to the design requirement of practical filter to main lobe and The performance requirement of secondary lobe automatically adjusts it is difficult to obtain meeting the wave filter of reality, in the face of minimization problem it is difficult to obtain Excellent solution, thus accordingly optimum wave filter design ratio can not be given.

Content of the invention

Based on this it is necessary to be directed to the problems referred to above, provide a kind of fir digital filter design method and system, can basis Actual wave filter design requirement automatically adjusts to the performance requirement of main lobe and secondary lobe, to obtain meeting the filtering of reality Device, and can quickly obtain optimal solution, thus providing accordingly optimum wave filter design ratio.

A kind of fir digital filter design method, comprises the steps:

Fir digital filter is modeled obtain with the mathematical model of wave filter according to wave filter design requirement；

The parameter restrictive condition of wave filter is carried out refine acquisition condition weighted model according to described mathematical model；

Solve described condition weighted model using genetic algorithm and method of least square and obtain optimum filter coefficient；

Obtain the fir digital filter meeting described actual filtering demands according to described filter coefficient.

A kind of fir digital filter design system, comprising:

Mathematical modeling module, for being modeled to fir digital filter obtaining wave filter according to wave filter design requirement Mathematical model；

Condition refinement module, obtains bar for the parameter restrictive condition of wave filter being carried out with refinement according to described mathematical model Part weighted model；

Model solution module, obtains optimum for solving described condition weighted model using genetic algorithm and method of least square Filter coefficient；

Wave filter designs module, for obtaining the fir number meeting described actual filtering demands according to described filter coefficient Word wave filter.

Above-mentioned fir digital filter design method and system, can enter to secondary lobe and main lobe according to actual different demands Row weighted sum, thus can get the wave filter design of different performance, Algorithm for Solving process is by genetic algorithm and method of least square Combine, can the optimum filter factor of overall fast search, obtain the wave filter of the optimum meeting actual demand, accelerate algorithm Convergence rate, improve the search precision of algorithm, such that it is able to obtain optimal filter design ratio, design optimum Fir digital filter.

Brief description

Fig. 1 is fir digital filter design method flow diagram of the present invention；

Fig. 2 is genetic algorithm flow chart；

Fig. 3 is fir digital filter design system structure diagram of the present invention.

Specific embodiment

Below in conjunction with the accompanying drawings the specific embodiment of the fir digital filter design method and system of the present invention is made in detail Description.

With reference to shown in Fig. 1, Fig. 1 is fir digital filter design method flow diagram of the present invention；Mainly comprise the steps:

Step s10, is modeled obtaining the mathematical modulo of wave filter according to wave filter design requirement to fir digital filter Type.

In this step, mainly according to actual different demands, secondary lobe and main lobe are weighted sue for peace, thus can obtain To the wave filter design of different performances, due in the design of wave filter, needing to ensure that frequency spectrum passes through main lobe, secondary lobe as far as possible Try one's best little to stop the spectral decay of this frequency range, using Minimum Mean Square Error it is impossible to be adjusted according to the actual requirements.

Therefore, in present invention design, it is filtered the design of device by the way of weighting, such that it is able to according to actual Design requirement automatically adjusts to the performance requirement of main lobe and secondary lobe, to obtain meeting the wave filter of reality.

In one embodiment, for the modeling method of step s10, specifically can be such that

First, set up the filter design model of weighting；Wherein, use h_d(e^jw) represent ideal filter frequency response, h (e^jw) Represent the filter freguency response actually obtaining, with e (e^jw) representing frequency response error, filter design model concrete form is such as Under:

e(e^jw)=h_d(e^jw)-h(e^jw). (1)

Calculate mean square error e², e²Expression formula is

$e^2=\frac{1}{2\mathrm{\π}}{\&integral;}_{-\mathrm{\π}}^{\mathrm{\π}}{\left|e\left(e^{\mathrm{jw}}\right)\right|}^2\mathrm{dw}=\frac{1}{2\mathrm{\π}}{\&integral;}_{-\mathrm{\π}}^{\mathrm{\π}}{|h_d\left(e^{\mathrm{jw}}\right)-h\left(e^{\mathrm{jw}}\right)|}^2\mathrm{dw}.---\left(2\right)$

Using fast Fourier transform (fft), above-mentioned two formulas are processed, can obtain

$\left\{\begin{array}{c}{h}_d\left(e^{\mathrm{jw}}\right)=\underset{n=\∞}{\overset{\∞}{\mathrm{\σ}}}{h}_d\left(n\right)e^{-\mathrm{jwn}}\\ h\left(e^{\mathrm{jw}}\right)=\underset{n=0}{\overset{n-1}{\mathrm{\σ}}}h\left(n\right)e^{-\mathrm{jwn}}\end{array}\right..---\left(3\right)$

Above formula (3) is substituted in mean square error formula (2), expression formula is as follows:

$\begin{array}{c}e\left(e^{\mathrm{jw}}\right)=h_d\left(e^{\mathrm{jw}}\right)-h\left(e^{\mathrm{jw}}\right)\\ =\underset{n=0}{\overset{n-1}{\mathrm{\σ}}}[h_d\left(n\right)-h\left(n\right)]e^{-\mathrm{jwn}}+\underset{n=n}{\overset{+\∞}{\mathrm{\σ}}}{h}_d\left(n\right)e^{-\mathrm{jwn}.}\end{array}---\left(4\right)$

According to Pa Saiwa formula, can obtain

$\begin{array}{c}{e}^2=\frac{1}{2\mathrm{\π}}{\&integral;}_{-\mathrm{\π}}^{\mathrm{\π}}{\left|e\left(e^{\mathrm{jw}}\right)\right|}^2\mathrm{dw}\\ =\underset{n=0}{\overset{n-1}{\mathrm{\σ}}}[h_d\left(n\right)-h\left(n\right)]e^{-\mathrm{jwn}}+\underset{n=n}{\overset{+\∞}{\mathrm{\σ}}}{h}_d\left(n\right)e^{-\mathrm{jwn}.}\end{array}---\left(5\right)$

In above formula, equation second left and formula are constant, and with design load h (n), n=0,1 ..., n-1 are unrelated；Make Obtain e²Minimum, only needs first and formula minimum, and here only needs to pay close attention to equation right-hand member Part I.

In order to obtain filter factor it is only necessary to m stepped-frequency signal w is taken on [- π, π]_k(k=0,1 ..., m-1), obtains One group of h (n), n=0,1 ..., n-1 so that

$\underset{k=0}{\overset{m-1}{\mathrm{\σ}}}{|\underset{n=0}{\overset{n-1}{\mathrm{\σ}}}h\left(n\right)e^{\mathrm{jn}{w}_k-h_d\left(w_k\right)}}^2---\left(6\right)$

Minimum, the value of acquisition is minimum wave filter design parameter value.

Further, simple and easily operated in order to calculate, solution procedure can be converted into the operation of matrix and vector, Specific as follows:

Order

$b={\left[\begin{array}{cccc}{e}^{-j{w}_1}& e^{-2j{w}_1}& \·\·\·& e^{-\mathrm{jn}{w}_1}\\ \·\·\·& \·\·\·& \·\·\·& \\ e^{-j{w}_i}& e^{-2j{w}_i}& \·\·\·& e^{-\mathrm{jn}{w}_i}\\ \·\·\·& \·\·\·& \·\·\·& \\ e^{-j{w}_m}& e^{-2j{w}_m}& \·\·\·& e^{-\mathrm{jn}{w}_m}\end{array}\right]}_{m\×n}---\left(7\right)$

Wherein, ξ=[h (0), h (1) ... h (n-1)]^t, h=[h_d(w₁),h_d(w₂),…,h_d(w_m)], then above-mentioned weighted filtering Design a model and be reduced to

$\min {\left|\right|b\·\mathrm{\ξ}-h\left|\right|}_2^2---\left(8\right)$

In formula,Represent two norms, for described two norms, i.e. x=(x₁,x₂,…,x_n), then ${\left|\right|x\left|\right|}_2^2=x_1^2+x_2^2+\·\·\·+x_n^2.$

It is to be understood that, above-mentioned modeling method and its mathematical model, are based on the preferred filter design setting up weighting Model method and its model representation form, are not limited to the technical scheme illustrate in above preferred embodiment in practice.

Step s20, carries out to the parameter restrictive condition of wave filter refining acquisition condition weighting mould according to described mathematical model Type.

In this step, the actual demand main forms being directed to wave filter design are main lobe and secondary lobe attention rate, According to the actual requirements the parameter restrictive condition of wave filter is refined, thus obtaining the weighted model under this restrictive condition.

In one embodiment, in order to improve fir performance of filter it is desirable to the main lobe width of window function is as narrow as possible, with Obtain narrower intermediate zone；The relative value of side lobe height is as little as possible, and quantity is as few as possible, with little, the stopband that obtains passband ripple Decay is big, all stable feature in passband and stopband, and the response of wave filter actual frequency so can be made preferably to approach preferable frequency Rate responds.

Concrete processing method is to first set up the weight function matrix of correlation, and concrete form is as follows

Wherein,Now, the weighted model of formula (8) is rewritten into

$\min {f\left|\right|a(b\·\mathrm{\ξ}-h)\left|\right|}_2^2---\left(10\right)$

In formula,Represent two norms, f is object function.

Need also exist for stating, the above-mentioned parameter restrictive condition to wave filter refines, be to be implemented based on preferred Example, is not limited to the technical scheme illustrate in above preferred embodiment in practice.

Step s30, solves described condition weighted model using genetic algorithm and method of least square and obtains optimum wave filter Coefficient.

In this step, will the genetic algorithm in evolution algorithm combine with conjugate gradient algorithms, thus can the overall situation fast The optimum filter factor of speed search.This algorithm makes full use of the ability of searching optimum of genetic algorithm and the quick office of conjugate gradient method Portion's search capability, accelerates the convergence rate of genetic algorithm, improves the search precision of genetic algorithm.Therefore, optimum can be drawn Wave filter design ratio.

Specifically, be rapid solving model optimal solution, the present invention is by the genetic algorithm in evolution algorithm and traditional classical Conjugate gradient algorithms improve and connected applications respectively, this paper abbreviation genetic algorithm.Respectively taken by relevant art means The advantage of algorithm, is solved using the ability of searching optimum of genetic algorithm and the Fast Convergent characteristic of conjugate gradient method.Pass through Conjugate gradient algorithms improve the convergence rate of genetic algorithm, so as to faster converge to accurate solution, are helped altogether by genetic algorithm Yoke gradient method jumps out locally optimal solution, and conjugate gradient method is embedded into genetic algorithm, need not be by all of in Population in Genetic Algorithms Body is performed both by conjugate gradient method, only need to consider to the individual execution in Population in Genetic Algorithms center conjugate gradient method.

In one embodiment, the method for concrete solving model acquisition filter coefficient comprises the steps:

Set up the model of genetic algorithm according to described weighted model；Specifically, population number is m, individual respectively a_i∈ rⁿ,i=1,2,…,m.

The group center of planting of described model is set to the initial search point that conjugate gradient algorithms are processed；Wherein, described center is The meansigma methodss of population at individual, expression formula is:M is population number, individual respectively a_i∈rⁿ,i=1,2,…,m；Due to Conjugate gradient method has quadratic terminability, and that is, for quadratic function, algorithm can terminate after n step iteration.

Execution n step conjugate gradient algorithms process and obtain result a⁽ⁿ⁾, calculate a⁽ⁿ⁾Fitness function, and according to a⁽ⁿ⁾Generate one Individuality, this individuality is added in population and replaces the minimum individuality of fitness value；Specifically, for non-quadratic function, execute n Step also can get preferable effect, therefore, by a₀Initial search point as conjugate gradient method simultaneously executes n step conjugate gradient method, Obtained result is a⁽ⁿ⁾.Calculate a⁽ⁿ⁾Fitness function, and according to a⁽ⁿ⁾Generate an individual and then be then added to population In, to replace the individuality of fitness value minimum, so that population scale remains m.

Circulation execution genetic algorithm iterative processing next time and conjugate gradient algorithms and process step, i.e. circulation executes mixing Genetic algorithm, until solving the optimal solution of weighted model, this optimal solution is set to filter coefficient.

In order to become apparent from the algorithmic procedure of step s30, illustrate algorithm examples below in conjunction with the accompanying drawings.

With reference to shown in Fig. 2, Fig. 2 is genetic algorithm flow chart, mainly comprises the steps:

Step a, initialization produce initial population；Wherein, setting population scale is m, and crossover probability is p_c, mutation probability is p_m, setting iterationses are n；

Step b, calculating individual adaptation degree function f, i.e. object function；

Step c, execution crossover operator and mutation operator；

Step d, the center a of calculating population₀；

Step e, the Searching point of initialization conjugate gradient algorithms, will a₀It is set to the initial ranging of conjugate gradient algorithms process Point；Wherein, k=1 is set, iterationses n is set₀, required precision ε is set, and executes following algorithm process:

If step fThen stop calculating；Otherwise putWherein, ${\mathrm{\β}}_{k-1}=\left\{\begin{array}{c}0,k=1\\ \frac{{\left|\right|\▿f\left(a^{\left(k\right)}\right)\left|\right|}^2}{{\left|\right|\▿f\left(a^{(k-1)}\right)\left|\right|}^2},k>1;\end{array}\right.$

Step g, carry out linear search, solve one-dimensional problem: max φ (a)=f (a^(k)+αd^(k)), obtain α_k, put a^(k)=a^(k) +a_kd^(k)；Make k=k+1, turn and go execution step f, and result of calculation is designated as a⁽ⁿ⁾；

Step h, calculating a⁽ⁿ⁾Fitness function, and according to a⁽ⁿ⁾Generate an individual, add in population, replace suitable in population The minimum individuality of response, turns and goes execution step c；

Step i, iteration terminate, and export optimal solution, are set to filter coefficient.

The above-mentioned genetic algorithm based on the present invention is it is only necessary to being alternately performed genetic algorithm to the center individuality of population and being total to Yoke gradient method, thus can make full use of the searching characteristic of genetic algorithm and the Fast Convergent characteristic of conjugate gradient method, Algorithm is enable rapidly to converge to optimal solution.

Step s40, obtains the fir digital filter meeting described actual filtering demands according to described filter coefficient.

In this step, mainly according to the calculated filter coefficient of preceding step, design meets actual demand Optimum fir digital filter.

Summary fir digital filter design method, according to actual different demands, is filtered by the way of weighting The design of ripple device, is weighted to secondary lobe and main lobe suing for peace, performance need that can be according to actual design requirement to main lobe and secondary lobe Ask and automatically adjust, thus can get the wave filter design of different performances；In derivation algorithm, in the face of minimization problem, Using genetic algorithm, the genetic algorithm in evolution algorithm is combined with traditional conjugate gradient algorithms, thus can the overall situation The optimum filter factor of fast search.This algorithm makes full use of the ability of searching optimum of genetic algorithm and the quick of conjugate gradient method Local search ability, accelerates the convergence rate of genetic algorithm, improves the search precision of genetic algorithm.Thus optimum can be drawn Wave filter design ratio, according to filter factor, can obtain the wave filter of the optimum meeting actual demand.

With reference to shown in Fig. 3, Fig. 1 is fir digital filter design system structure diagram of the present invention；Specifically include that

Mathematical modeling module 10, for being modeled to fir digital filter obtaining filtering according to wave filter design requirement The mathematical model of device；

Condition refinement module 20, obtains for the parameter restrictive condition of wave filter being carried out with refinement according to described mathematical model Condition weighted model；

Model solution module 30, obtains for solving described condition weighted model using genetic algorithm and method of least square Excellent filter coefficient；

Wave filter designs module 40, for obtaining the fir meeting described actual filtering demands according to described filter coefficient Digital filter.

In one embodiment, mathematical modeling module 10 is further used for:

Filter design model according to the input foundation weighting of wave filter design requirement:

e(e^jw)=h_d(e^jw)-h(e^jw).

In formula, h_d(e^jw) represent ideal filter frequency response, h (e^jw) represent the filter freguency response actually obtaining, e (e^jw) represent frequency response error；

Calculate mean square eikonal equation:

$e^2=\underset{n=0}{\overset{n-1}{\mathrm{\σ}}}[h_d\left(n\right)-h\left(n\right)]e^{-\mathrm{jwn}}+\underset{n=n}{\overset{+\∞}{\mathrm{\σ}}}{h}_d\left(n\right)e^{-\mathrm{jwn}}.$

In formula, e²Represent mean square error, wherein:

$\left\{\begin{array}{c}{h}_d\left(e^{\mathrm{jw}}\right)=\underset{n=\∞}{\overset{\∞}{\mathrm{\σ}}}{h}_d\left(n\right)e^{-\mathrm{jwn}}\\ h\left(e^{\mathrm{jw}}\right)=\underset{n=0}{\overset{n-1}{\mathrm{\σ}}}h\left(n\right)e^{-\mathrm{jwn}}\end{array}\right..$

Mathematical model according to mean square eikonal equation acquisition wave filter:

$\min {\left|\right|b\·\mathrm{\ξ}-h\left|\right|}_2^2$

Wherein:

ξ=[h(0),h(1),…h(n-1)]^t,

h=[h_d(w₁),h_d(w₂),…,h_d(w_m)]

$b={\left[\begin{array}{cccc}{e}^{-j{w}_1}& e^{-2j{w}_1}& \·\·\·& e^{-\mathrm{jn}{w}_1}\\ \·\·\·& \·\·\·& \·\·\·& \\ e^{-j{w}_i}& e^{-2j{w}_i}& \·\·\·& e^{-\mathrm{jn}{w}_i}\\ \·\·\·& \·\·\·& \·\·\·& \\ e^{-j{w}_m}& e^{-2j{w}_m}& \·\·\·& e^{-\mathrm{jn}{w}_m}\end{array}\right]}_{m\×n}$

In formula,Represent two norms, w_kM stepped-frequency signal on [- π, π] for (k=0,1 ..., m-1) expression, h (n), N=0,1 ..., n-1 makes formula for one group:The value obtaining is minimum wave filter design parameter Value.

In one embodiment, condition refinement module 20 is further used for:

Set up the related weight function matrix a of wave filter actual frequency response:

Wherein, a is weight function matrix,

According to weight function matrix a calculating weighted model:

In formula,Represent two norms, f is object function.

In one embodiment, model solution module 30 is further used for:

Set up the model of genetic algorithm according to described weighted model；

The center of the population of described model is set to the initial search point of conjugate gradient algorithms process；Wherein, described center For the meansigma methodss of population at individual, expression formula is:M is population number, individual respectively a_i∈rⁿ,i=1,2,…,m；

Execution n step conjugate gradient algorithms process and obtain result a⁽ⁿ⁾, calculate a⁽ⁿ⁾Fitness function, and according to a⁽ⁿ⁾Generate one Individuality, this individuality is added in population and replaces the minimum individuality of fitness value；

Circulation execution genetic algorithm iterative processing next time and conjugate gradient algorithms process step, until solve weighting mould The optimal solution of type, is set to filter coefficient.

Further, model solution module 30 specifically includes for the algorithm solving described condition weighted model:

A, initialization produce initial population；Wherein, setting population scale is m, and crossover probability is p_c, mutation probability is p_mIf, Putting iterationses is n；

B, calculating individual adaptation degree function f；

C, execution crossover operator and mutation operator；

D, the center a of calculating population₀；

E, by a₀It is set to the initial search point of conjugate gradient algorithms process；Wherein, k=1 is set, iterationses n is set₀If, Put required precision ε, and execute following algorithm process:

If fThen stop calculating；Otherwise putWherein, ${\mathrm{\β}}_{k-1}=\left\{\begin{array}{c}0,k=1\\ \frac{{\left|\right|\▿f\left(a^{\left(k\right)}\right)\left|\right|}^2}{{\left|\right|\▿f\left(a^{(k-1)}\right)\left|\right|}^2},k>1;\end{array}\right.$

G, carry out linear search, solve One Dimension Optimization Problems: max φ (α)=f (a^(k)+αd^(k)), obtain α_k, put a^(k)=a^(k) +α_kd^(k)；Make k=k+1, turn and go execution step f, and result of calculation is designated as a⁽ⁿ⁾；

H, calculating a⁽ⁿ⁾Fitness function, generate new population, that is, according to a⁽ⁿ⁾Generate an individual, add in population, Replace the minimum individuality of fitness in population, turn and go execution step c；

I, iteration terminate, and export optimal solution, are set to filter coefficient.

The fir digital filter design system of the present invention is corresponded with the fir digital filter design method of the present invention, All it is applied to fir numeral in the technical characteristic of the embodiment elaboration of above-mentioned fir digital filter design method and its advantage In the embodiment of wave filter design system, hereby give notice that.

Embodiment described above only have expressed the several embodiments of the present invention, and its description is more concrete and detailed, but simultaneously Therefore the restriction to the scope of the claims of the present invention can not be interpreted as.It should be pointed out that for those of ordinary skill in the art For, without departing from the inventive concept of the premise, some deformation can also be made and improve, these broadly fall into the guarantor of the present invention Shield scope.Therefore, the protection domain of patent of the present invention should be defined by claims.

Claims (10)

1. a kind of fir digital filter design method is it is characterised in that comprise the steps:

Fir digital filter is modeled obtain with the mathematical model of wave filter according to wave filter design requirement；Described mathematical modulo Type is:

$\begin{array}{cc}\min & \left|\right|b\·\mathrm{\ξ}-h|{|}_2^2\end{array}$

Wherein:

ξ=[h (0), h (1), k h (n-1)]^t,

H=[h_d(w₁),h_d(w₂),k,h_d(w_m)]

$b={\left[\begin{array}{cccc}{e}^{-{\mathrm{jw}}_1}& e^{-2{\mathrm{jw}}_1}& l& e^{-{\mathrm{jnw}}_1}\\ l& l& l& \\ e^{-{\mathrm{jw}}_i}& e^{-2{\mathrm{jw}}_i}& l& e^{-{\mathrm{jnw}}_i}\\ l& l& l& \\ e^{-{\mathrm{jw}}_m}& e^{-2{\mathrm{jw}}_m}& l& e^{-{\mathrm{jnw}}_m}\end{array}\right]}_{m\×n}$

In formula,Represent two norms, w_k(k=0,1, λ, m-1) represents m stepped-frequency signal on [- π, π], h (n), n= 0,1, λ, n-1 make formula for one group:The value obtaining is minimum wave filter design parameter value；

The parameter restrictive condition of wave filter is carried out refine acquisition condition weighted model according to described mathematical model；Described weighting mould Type is:In formula,Represent two norms, f is object function, wherein,

Solve described condition weighted model using genetic algorithm and method of least square and obtain optimum filter coefficient；

Obtain the fir digital filter meeting described actual filtering demands according to described filter coefficient.

2. fir digital filter design method according to claim 1 is it is characterised in that according to wave filter design requirement The step that fir digital filter is modeled obtain with the mathematical model of wave filter includes:

Filter design model according to the input foundation weighting of wave filter design requirement:

e(e^jw)=h_d(e^jw)-h(e^jw).

In formula, h_d(e^jw) represent ideal filter frequency response, h (e^jw) represent the filter freguency response actually obtaining, e (e^jw) Represent frequency response error；

Calculate mean square eikonal equation:

$e^2=\underset{n=0}{\overset{n-1}{\σ}}\[h_d\left(n\right)-h\left(n\right)\]e^{-jwn}+\underset{n=n}{\overset{+\mathrm{\∞}}{\σ}}{h}_d\left(n\right)e^{-jwn}.$

In formula, e²Represent mean square error, wherein:

$\left\{\begin{array}{c}{h}_d\left(e^{jw}\right)=\underset{n=-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\mathrm{\σ}}}{h}_d\left(n\right)e^{-jwn}\\ h\left(e^{jw}\right)=\underset{n=0}{\overset{n-1}{\mathrm{\σ}}}h\left(n\right)e^{-jwn}\end{array}\right..$

Obtain the mathematical model of wave filter according to mean square eikonal equation.

3. fir digital filter design method according to claim 1 is it is characterised in that according to described mathematical model pair The step that the parameter restrictive condition of wave filter carries out refining acquisition condition weighted model includes:

Set up the related weight function matrix α of wave filter actual frequency response, weighted model is calculated according to weight function matrix α.

4. fir digital filter design method according to claim 1 is it is characterised in that utilize genetic algorithm and minimum The step that square law solves the filter coefficient that described condition weighted model obtains optimum includes:

Set up the model of genetic algorithm according to described weighted model；

The group center of planting of described model is set to the initial search point that conjugate gradient algorithms are processed；Wherein, described center is population Individual meansigma methodss, expression formula is:M is population number, individual respectively a_i∈rⁿ, i=1,2, k, m；

Execution n step conjugate gradient algorithms process and obtain result a⁽ⁿ⁾, calculate a⁽ⁿ⁾Fitness function, and according to a⁽ⁿ⁾Generate one Individuality, this individuality is added in population and replaces the minimum individuality of fitness value；

Circulation execution genetic algorithm iterative processing next time and conjugate gradient algorithms process step, until solve weighted model Optimal solution, is set to filter coefficient.

5. fir digital filter design method according to claim 4 is it is characterised in that utilize genetic algorithm and minimum The step that square law solves the filter coefficient that described condition weighted model obtains optimum specifically includes:

A, initialization produce initial population；Wherein, setting population scale is m, and crossover probability is p_c, mutation probability is p_m, setting changes Generation number is n；

B, calculating individual adaptation degree function f；

C, execution crossover operator and mutation operator；

D, the center a of calculating population₀；

E, by a₀It is set to the initial search point of conjugate gradient algorithms process；Wherein, k=1 is set, iterationses n is set₀, setting essence Degree requires ε, and executes following algorithm process:

If fThen stop calculating；Otherwise putWherein,

G, carry out linear search, solve one-dimensional problem: max φ (α)=f (a^(k)+αd^(k)), obtain α_k, put a^(k)=a^(k)+α_kd^(k)； Make k=k+1, turn and go execution step f, and result of calculation is designated as a⁽ⁿ⁾；

H, calculating a⁽ⁿ⁾Fitness function, generate new population, that is, according to a⁽ⁿ⁾Generate an individual, add in population, replace The minimum individuality of fitness in population, turns and goes execution step c；

I, iteration terminate, and export optimal solution, are set to filter coefficient.

6. a kind of fir digital filter design system is it is characterised in that include:

Mathematical modeling module, for being modeled obtaining the number of wave filter according to wave filter design requirement to fir digital filter Learn model；Described mathematical model is:

$\begin{array}{cc}\min & \left|\right|b\·\mathrm{\ξ}-h|{|}_2^2\end{array}$

Wherein:

ξ=[h (0), h (1), k h (n-1)]^t,

H=[h_d(w₁),h_d(w₂),k,h_d(w_m)]

$b={\left[\begin{array}{cccc}{e}^{-{\mathrm{jw}}_1}& e^{-2{\mathrm{jw}}_1}& l& e^{-{\mathrm{jnw}}_1}\\ l& l& l& \\ e^{-{\mathrm{jw}}_i}& e^{-2{\mathrm{jw}}_i}& l& e^{-{\mathrm{jnw}}_i}\\ l& l& l& \\ e^{-{\mathrm{jw}}_m}& e^{-2{\mathrm{jw}}_m}& l& e^{-{\mathrm{jnw}}_m}\end{array}\right]}_{m\×n}$

In formula,Represent two norms, w_k(k=0,1, λ, m-1) represents m stepped-frequency signal on [- π, π], h (n), n= 0,1, λ, n-1 make formula for one group:The value obtaining is minimum wave filter design parameter Value；

Condition refinement module, adds for the parameter restrictive condition of wave filter being carried out with refinement acquisition condition according to described mathematical model Power model；Described weighted model is:In formula,Represent two norms, f is object function, wherein,

Model solution module, obtains optimum filter for solving described condition weighted model using genetic algorithm and method of least square Ripple device coefficient；

Wave filter designs module, for obtaining the fir numeral filter meeting described actual filtering demands according to described filter coefficient Ripple device.

7. fir digital filter design system according to claim 6 is it is characterised in that mathematical modeling module is further For:

Filter design model according to the input foundation weighting of wave filter design requirement:

e(e^jw)=h_d(e^jw)-h(e^jw).

In formula, h_d(e^jw) represent ideal filter frequency response, h (e^jw) represent the filter freguency response actually obtaining, e (e^jw) Represent frequency response error；

Calculate mean square eikonal equation:

$e^2=\underset{n=0}{\overset{n-1}{\σ}}\[h_d\left(n\right)-h\left(n\right)\]e^{-jwn}+\underset{n=n}{\overset{+\mathrm{\∞}}{\σ}}{h}_d\left(n\right)e^{-jwn}.$

In formula, e²Represent mean square error, wherein:

$\left\{\begin{array}{c}{h}_d\left(e^{jw}\right)=\underset{n=-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\mathrm{\σ}}}{h}_d\left(n\right)e^{-jwn}\\ h\left(e^{jw}\right)=\underset{n=0}{\overset{n-1}{\mathrm{\σ}}}h\left(n\right)e^{-jwn}\end{array}\right..$

Obtain the mathematical model of wave filter according to mean square eikonal equation.

8. fir digital filter design system according to claim 6 is it is characterised in that condition refinement module is further For:

Set up the related weight function matrix α of wave filter actual frequency response, weighted model is calculated according to weight function matrix α.

9. fir digital filter design system according to claim 6 is it is characterised in that model solution module is further For:

Set up the model of genetic algorithm according to described weighted model；

The group center of planting of described model is set to the initial search point that conjugate gradient algorithms are processed；Wherein, described center is population Individual meansigma methodss, expression formula is:M is population number, individual respectively a_i∈rⁿ, i=1,2, k, m；

Execution n step conjugate gradient algorithms process and obtain result a⁽ⁿ⁾, calculate a⁽ⁿ⁾Fitness function, and according to a⁽ⁿ⁾Generate one by one Body, this individuality is added in population and replaces the minimum individuality of fitness value；

Circulation execution genetic algorithm iterative processing next time and conjugate gradient algorithms process step, until solve weighted model Optimal solution, is set to filter coefficient.

10. fir digital filter design system according to claim 9 is it is characterised in that model solution module is used for asking The algorithm solving described condition weighted model specifically includes:

A, initialization produce initial population；Wherein, setting population scale is m, and crossover probability is p_c, mutation probability is p_m, setting changes Generation number is n；

B, calculating individual adaptation degree function f；

C, execution crossover operator and mutation operator；

D, the center a of calculating population₀；

E, by a₀It is set to the initial search point of conjugate gradient algorithms process；Wherein, k=1 is set, iterationses n is set₀, setting essence Degree requires ε, and executes following algorithm process:

If fThen stop calculating；Otherwise putWherein,

G, carry out linear search, solve One Dimension Optimization Problems: max φ (α)=f (a^(k)+αd^(k)), obtain α_k, put a^(k)=a^(k)+α_kd^(k)；Make k=k+1, turn and go execution step f, and result of calculation is designated as a⁽ⁿ⁾；

H, calculating a⁽ⁿ⁾Fitness function, generate new population, that is, according to a⁽ⁿ⁾Generate an individual, add in population, replace The minimum individuality of fitness in population, turns and goes execution step c；

I, iteration terminate, and export optimal solution, are set to filter coefficient.