Help IFFT can not restore to original signal after filtering
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I tried to compare original signal and signal after high pass filter using ifft. but the result seems odd to me. Can anyone explain why its happened
here is my code
%USING REAL SIGNAL
data_full=load("sig_tremor.txt");
data=data_full(:,2);
srate=100;
t=data_full(:,1);
n=length(t);
figure(1)
subplot(211), plot(t,data), hold on
% HIGH PASS FILTER (SIGNAL*KERNEL)
X=fft(data);
hz=linspace(0,srate,n);
subplot(212), plot(hz,2*abs(X)/n,'-b')
hold on, set(gca,'xlim',[0 10])
% applying high pass filter --> multiplied by kernel
% hz+10 indicate how high freq can be passed
filterkernel = (1./(1+exp(-hz+1)));
XHP=X.*filterkernel;
subplot(211), plot(t,real(ifft(XHP)),'r')
xlabel('Time'), ylabel('Amplitude')
legend('original','HP filter')
subplot(212), plot(hz,2*abs(XHP)/n,'r')
set(gca,'xlim',[0 10],'xtick',[0:2:25])
xlabel('Frequency')
legend('original','HP filter')
hold off
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Star Strider
2023-8-28
The fftfilt function can do this relatively efficiently, however since you want to do it manually, try this —
%USING REAL SIGNAL
data_full=load("sig_tremor.txt");
data=data_full(:,2);
% srate=100;
t=data_full(:,1);
srate = 1/mean(diff(t));
n=length(t);
figure(1)
subplot(211), plot(t,data), hold on
% HIGH PASS FILTER (SIGNAL*KERNEL)
X=fft(data);
size(X)
hz=linspace(0,srate,n);
hz2=linspace(0,(n/2)-1,fix(n/2))*2/srate;
subplot(212), plot(hz,2*abs(X(1:numel(hz)))/n,'-b')
hold on, set(gca,'xlim',[0 10])
% applying high pass filter --> multiplied by kernel
% hz+10 indicate how high freq can be passed
filterkernel = (1./(1+exp(-(hz(1:fix(n/2))+1)))).';
figure
plot(filterkernel)
grid
xlim([0 100])
title('Filter passband')
Xs = fftshift(X);
n2 = fix(n/2)
XHP = [Xs(1:n2).*flip(filterkernel); Xs(n2+1:end).*filterkernel];
XHPs = ifftshift(XHP);
XHPi = ifft(XHPs);
Fs = srate;
Fv = linspace(-Fs/2, Fs/2-Fs/length(X), length(X)); % EVEN 'length(X)' (Asymmetric)
% XHP=X.*filterkernel;
figure
subplot(211), plot(t,real(ifft(XHPs)),'r')
xlabel('Time'), ylabel('Amplitude')
title('original')
subplot(212), plot(hz,2*abs(XHPs)/n,'r')
set(gca,'xlim',[0 10],'xtick',[0:2:25])
xlabel('Frequency')
title('HP filter')
hold off
figure
plot(t-t(1),real(XHPi),'r', 'DisplayName','HP filter')
hold on
plot(t-t(1), data, 'b', 'DisplayName','Original')
hold off
set(gca,'xlim',[0 10],'xtick',[0:2:25])
xlabel('Time')
hold off
legend('Location','best')
It was difficult to figure you what you are doing here, so I had to make some changes.
The filter itself actually does not do much to the signal.
.
2 个评论
Star Strider
2023-8-28
My pleasure!
If my Answer helped you solve your problem, please Accept it!
If you want to use filtfilt with the filter you created, first use a vector created from it (such as I created in the second figure here, with an associated frequency vector and the requested filter order) it as inputs to the firls function. That will create a FIR filter that should closely match it.
.
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