FFT and smoothing of signal

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Isma_gp
Isma_gp 2017-1-16
评论： Star Strider 2022-12-2
Hi, I have the attached signal (TENS_LOW). I would like to obtained the smoothed FFT of the signal. How can I smooth the spectrum?
Thanks
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Adam
Adam 2017-1-16
How to smooth the spectrum depends what you want to do with it really. There are plenty of ways to do it, depending how aggressive you want to be. A simple mean filter would do if you just want aggressive smoothing, but not if you want to retain certain information in peaks etc
Isma_gp
Isma_gp 2017-1-16
sampling frequency is 0.0117

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Star Strider
Star Strider 2017-1-16
Now I understand what you want to do. This is most easily done with the Signal Processing Toolbox sgolayfilt function to create the Savitzky-Golay filtered spectrum.
The Code —
D = load('Isma_gp TENS_LOW.mat');
sig = D.TENS_LOW_42;
sig = sig - mean(sig); % Remove d-c Offset
L = length(sig);
Fs = 1/0.0117; % Sampling Frequency
Fn = Fs/2; % Nyquist Frequency
FTsig = fft(sig)/L;
Fv = linspace(0, 1, fix(length(FTsig)/2)+1)*Fn; % Frequency Vector
Iv = 1:length(Fv); % Index Vector
FTsiga = double(abs(FTsig(Iv))*2); % Truncate, Magnitude, Convert To Double
sgf_sm = sgolayfilt(FTsiga, 5, 501); % Create ‘sgolayfilt’ Filtered FFT
figure(1)
plot(Fv, FTsiga)
hold on
plot(Fv, sgf_sm, '-r', 'LineWidth',2)
hold off
axis([0 1 ylim])
grid
xlabel('Frequency')
ylabel('Amplitude')
legend('Original Spectrum', 'Savitzky-Golay Filtered Spectrum')
Experiment with the sgolayfilt parameters to get the result you want.
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SYML2nd
SYML2nd 2022-12-1
Hi @Star Strider, I think this is a brilliant solution to smooth the fft for which there are not so much other oprions to smooth it, such as for the PSD where we can use pwelch and a windowing. Are there any reference (literature) where this method of smoothing is used?
Star Strider
Star Strider 2022-12-2
@SYML2nd — Not to my knowledge, although I did not do a literature search. My approach here is essentially empirical.

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