How to apply a Farrow structure delay filter(FIR) to a signal in Matlab?

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chen jiyuan 2021-2-7

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/738147-how-to-apply-a-farrow-structure-delay-filter-fir-to-a-signal-in-matlab

评论： Star Strider 2021-3-6

For a signal, which is very common, just like this one

t=linspace(0,100e-6,1024);
k=10e13;
y=exp(-1i*k*pi*t.^2);

The function in the signal processing toolbox of MATLAB is used to generate a delay filter with Farrow structure, and the filter coefficients are obtained.

L=18;
d = fdesign.fracdelay(abs(Delay),'N',L);
farrow = design(d, 'lagrange', 'FilterStructure', 'farrowfd');
farrow_coff=farrow.Coefficients;

Is it because the previous delay filter is not correct, the function filter can not correctly filter to obtain the desired results?

Or please give me a simulation example for reference.

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Answer 1

Star Strider 2021-2-7

1
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/738147-how-to-apply-a-farrow-structure-delay-filter-fir-to-a-signal-in-matlab#answer_616917

在 MATLAB Online 中打开

I cannot run your code because:

Unrecognized function or variable 'Delay'.

and ‘L’ is missing as well.

However, if you need to do phase-neutral digital filtering, use the filtfilt function instead of filter.

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chen jiyuan 2021-2-27

编辑：chen jiyuan 2021-2-27

在 MATLAB Online 中打开

Thank you very much for your answer. What I want to use this code is in wideband digital array beamforming. In this processing, each channel have to delay (fraction delay) to sum the final beam.

The flow chat is shown here.

The code is here

clear all;close all;
%% Paras Set
f0=15e9; 
B=2e9;
tau=100e-6; %pulse duration 
k=B/tau;
fmax=f0+B;
fmin=f0;
M=64;%number of Array 
fs=1e6;
N_r=tau*fs;%sampling points
R=15e2+10;%target distance
R_ref=15e2;%referee distance
c=3e8;
lambda0=c/fmax;
d=0.5*lambda0;% array space
theta_s=10;
theta_num=1024;
theta=linspace(-90,90,theta_num);
%% Echo signal and reference signal
%First, the array elements are calculated, and then the whole array is synthesized
t=linspace(0,tau,N_r);
f=linspace(fmin,fmax,N_r);
delay_r=2*R/c;
delay_ref=2*R_ref/c;
s_ref=exp(1i*2*pi*fmin*(t-delay_ref)+1i*2*pi*k*(t-delay_ref).^2); %refence signal
s_sum=0;
for m=1:M
    
    for i=1:theta_num
        delay_m=(m-1)*d*sind(theta_s)/c;
        delay=delay_r+delay_m;%Echo signal delay consists of two parts
        delay_com=(m-1)*d*sind(theta(i))/c; 
%         h_delay=dirac(t-(m-1)*d*sind(theta_s)/c);
         s_r=exp(1i*2*pi*fmin*(t-delay)+1i*2*pi*k*(t-delay).^2);  %Radar echo signal
         s_array=s_r.*conj(s_ref);%Mixing operation
         for j=1:N_r
            %%%%Phase compensation factor            
            s_com(j)=exp(1i*pi*(2*k*delay_com*t(j)+2*fmin*delay_com-k*delay_com.^2-2*k*delay_com*delay_ref));         
         end
        s(i,:)=s_array.*s_com;%compensate the phase
        
        % how to achieve time delay for each array?? dose not work
%         farrow_coff=Farrow_Coff(delay_com,4);
%         s(i,:)=fftfilt(s(i,:),farrow_coff);
%         s(i,:)=Farrow_Delay(s(i,:),farrow_coff);
    end
    s_sum=s_sum+s;%Synthesize the whole array
end
%%
figure
% plot(theta,s_sum(:,N_r));
mesh(theta,f,abs(s_sum.'));
% view(2);
figure
plot(theta,abs(s_sum(:,1)));hold on
plot(theta,abs(s_sum(:,N_r)));
plot(theta,abs(s_sum(:,N_r/2)));