how to smooth or filter the signal like this?

How to smooth the signal like this？

I want to do fourier transform of the data attached. I only need the sharp peak in the data, I don't know how to

filter the noise in the data. what about Hanning window or something else?

Your help would be highly appreciated.

Best regards

load('data.mat')
plot(t,dip)

Warning: Imaginary parts of complex X and/or Y arguments ignored.

Answer 1

[Bora Eryilmaz]

You can apply a low-pass filter to remove the noise in the signal before taking the Fourier Transform of the data:

load('data.mat')
plot(t,dip)

Warning: Imaginary parts of complex X and/or Y arguments ignored.

hold on
Fs = 1/(t(2)-t(1));
[b,a] = butter(4, 0.03/(Fs/2), 'low');
y = filter(b,a, real(dip));
plot(t,y)

By the way, your original data, dip, seems to have imaginary values in it. You would probably want to get rid of those.

Answer 2

[Daniel Niu]

@Star Strider

Dear Strider,

I see an answer from you by Email. But I can not see the answer here.

Would you mind post your answers again?

I need the fft of the signal seem to be peak with even distance like this.

Thank you!

Answer 3

[Star Strider]

I saved that code.

I did not save the non-code text that went with it. I am not certain that I can reproduce the image that you posted, because I do not understand what it is or how it was calculated. I plotted the Fourier transform three times here, once with the absolute amplitude, once with the amplitude in decibels, and once with the log amplitude.

Reposted —

LD = load(websave('data','https://www.mathworks.com/matlabcentral/answers/uploaded_files/1236142/data.mat'));
t = LD.t(:);
dip = LD.dip(:);

figure
plot(t, real(dip))
grid
xlabel('t')
ylabel('AMplitude')
title('Original Signal')
xlim([min(t) max(t)])

Ts = mean(diff(t));                                         % Sampling Interval
Fs = 1/Ts;                                                  % Sampling Frequency
Fn = Fs/2;                                                  % Nyquist Frequency
L = numel(t);
NFFT = 2^nextpow2(L);                                       % For Efficiency
FTdip = fft(dip-mean(dip).*hamming(L),NFFT)/L;              % Windowed Fourier Transform
Fv = linspace(0, 1, NFFT/2+1)*Fn;                           % Frequency Vector
Iv = 1:numel(Fv);                                           % Index Vector

figure
plot(Fv, abs(FTdip(Iv))*2, 'DisplayName','Data')
grid
xlabel('Frequency')
ylabel('Magnitude (Absolute)')
title('One-Sided Fourier Transform')
% xlim([0 0.5])

[maxPeak,idx] = max(abs(FTdip(Iv))*2)

maxPeak = 0.0804

idx = 225

maxPeakFreq = Fv(idx)

maxPeakFreq = 0.0273

passband = maxPeakFreq*[0.75 1.25]

passband = 1×2

0.0205 0.0342

xline(passband, '-r', 'DisplayName','Passband')
legend('Location','best')

figure
plot(Fv, mag2db(abs(FTdip(Iv))*2), 'DisplayName','Data')
grid
xlabel('Frequency')
ylabel('Magnitude (dB)')
title('One-Sided Fourier Transform')
% xlim([0 0.5])
xline(passband, '-r', 'DisplayName','Passband')
legend('Location','best')

figure
semilogy(Fv, abs(FTdip(Iv))*2, 'DisplayName','Data')
grid
xlabel('Frequency')
ylabel('Magnitude')
title('One-Sided Fourier Transform')
% xlim([0 0.5])
xline(passband, '-r', 'DisplayName','Passband')
legend('Location','best')

filtered_dip = bandpass(real(dip), passband, Fs, 'ImpulseResponse','iir');

figure
plot(t, filtered_dip)
grid
xlabel('t')
ylabel('Amplitude')
title('Filtered Signal')
xlim([min(t) max(t)])

This code selects the maximum frequency and defines a passband based on it. It then filters the signal using that passband. (The passband is also depicted in the frequency domain plot to illustrate what that filter passes.) I do not suggest a narrower passband, however shifting the existing passband or enlarging it (or both) are straightforward.

EDIT — (19 Dec 2022 at 20:36)

Looking at thid further, I am not certain how to get the result you want from this isgnal. The Savitzky-Golay filter (sgolayfilt) may be the way to go on it (another option being a FIR comb filter), however it is not obvious to me how to get the result depicted in your latest plot image.

% new_dip = lowpass(real(dip), 0.1, Fs, 'ImpulseResponse','iir')
sgfilt_dip = sgolayfilt(real(dip), 3, 127);

figure
plot(t, sgfilt_dip)
grid
xlabel('t')
ylabel('Amplitude')
title('Savitzky-Golay Filtered Signal')
xlim([min(t) max(t)])

FTdip = fft(sgfilt_dip-mean(sgfilt_dip).*hamming(L),NFFT)/L;              % Windowed Fourier Transform

figure
semilogy(Fv, abs(FTdip(Iv))*2, 'DisplayName','Data')
grid
xlabel('Frequency')
ylabel('Magnitude')
title('One-Sided Fourier Transform Of Savitzky-Golay Filtered Signal')
% xlim([0 0.5])
xline(passband, '-r', 'DisplayName','Passband')
legend('Location','best')

Experiment with the sgolayfilt function. Also, it would help if you described in some detail the result you want, since that is not obvious to me.

.

Answer 4

[Image Analyst]

Not sure what you consider a sharp peak. Is it anything above 0.25 or below -0.25? If so, you can just zero out everything with a magnitude less than 0.25:

load('data.mat')
dip(abs(dip) < 0.25) = 0;
plot(t, dip)

Then do whatever you want, such as filtering in the spectral domain.