Help IFFT can not restore to original signal after filtering

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

Answer 1

[Star Strider]

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)

ans = 1×2

1600 1

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)

n2 = 800

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.

.

[nirwana]

thanks a lot for nice answer. while waiting, i endup find solution of my code, that is I put transpose kernel filter. But still your code explain better.

NB : i just expolore how to write filter manually as part of training from book, i'll try to use filtfilt as u'r suggestion

[Star Strider]

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.

.