# How to smooth a FFT signal?

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Wakeel Mohammed on 20 Jan 2021
Commented: Star Strider on 21 Jan 2021
I managed to plot the FFT spectrum using the below code. But I couldn't plot the smoothed spectrum. Can anyone suggest me a way to go through it? and How to choose order and frame length for the sgolayfilt code.
clc
t = data (1:1024,1); %Selecting Time vector
s = data (1:1024,4); %Selecting Z axis vibrations
L = numel(t); %Signal length
Ts = mean(diff(t)); %Sampling interval
Fs = 1/Ts; %Sampling frequency
Fn = Fs/2; %Nyquist frequency
FTs = fft(s)/L; %Fast fourier transform (s- data)
Fv = linspace(0,1, fix(L/2)+1)*Fn; %Frequency vector
Iv = 1:numel(Fv); %Index vector
IV = Iv-mean(Iv);
FTsiga = double(abs(FTs(Iv))*2); %Magnitude,Convert to double
S_smth = sgolayfilt(FTsiga,20,501); %Savitzky-Golay filtering of FFT
h = figure(1);
subplot(4, 1, 1); %plotting top pane
plot(t,s); %Acceleration vs time
set(gca,'xlim',[1 51.2]); %Scale to fit
grid; %Grids on
title ({'Graph 5','Acceleration vs time'});
xlabel('time(s)');
ylabel('Acceleration (m/s^2)');
subplot(4, 1, 2); %Plotting bottom pane
plot(Fv, abs(FTs(Iv))*2,'red'); %FFT - Amplitude vs Frequency
grid
title ('Fast fourier transform');
xlabel('Frequency (Hz)');
ylabel ('Amplitude (m)');
subplot(4, 1, 3); %FFT
% plot(Fv, abs(FTs(Iv))*2,'red'); %FFT - Amplitude vs Frequency
% grid
% title ('Fast fourier transform');
% xlabel('Frequency (kHz)');
% ylabel ('Amplitude (m)');
% hold on
Y = fft(s-mean(s)); %Subtracting the mean before FFT to remove DC
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
plot(Fv,P1,'Green');
title ('Fast Fourier Transform - "DC removed"');
xlabel('Frequency (Hz)');
ylabel ('Amplitude (m)');
subplot(4,1,4); %Plotting filtered FFT
plot (Fv,S_smth,'-k');
title ('Fast Fourier Transform - "Filtered"');
xlabel('Frequency (kHz)');
ylabel ('Amplitude (m)');
% fig = figure(1);
% print(fig, 'myFileName.pdf', '-dpdf','-r0')
% saveas (h,'Graph5.png')
% saveas (h,'Graph5.eps')
% saveas (h,'Graph5.jpg')
Star Strider on 21 Jan 2021
Thank you!

R2018b

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