MATLAB: FFT of a Signal

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Hi, I would like to take the FFT of a signal but for some reason I do something wrong.

May someone could help me out?

I would like to see the FFT Spectrum for 2 seconds.

I attached the Excel file and the code.

Thanks!

Best Answer

The constant (‘direct current’ or ‘d-c’ 0 Hz) offset is hiding the rest of your spectrum. This is a common problem, and since removing the constant offset does not affect the rest of your signal (and you can easily recover it if needed, since it is the mean of your signal), remove it before calculating the fft to see the rest of your spectrum.

This works:

[d,s] = xlsread('Good State.xls');
Time = d(:,1);
Good = d(:,2);
L = size(d,1);                                              % Vector Length
Ts = mean(diff(Time));                                      % Sampling Interval (Assume ‘seconds’)
Fs = 1/Ts;                                                  % Sampling Frequency (Assume ‘Hz’)
Fn = Fs/2;                                                  % Nyquist Frequency (Assume ‘Hz’)
Good = Good - mean(Good);                                   % Remove D-C (Constant) Offset
Y = fft(Good)/L;                                            % Scaled Two-Sided Discrete Fourier Transform
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                         % Frequency Vector
Iv = 1:length(Fv);                                          % Index Vector For Plot
figure(1)
plot(Fv, 2*abs(Y(Iv)))
grid
xlabel('Frequency')
ylabel('Magnitude')

Related Solutions

MATLAB: FFT conversion of sound pressure in the time domain.

I prefer this documentation for fft. Specifically note the code between the tip two plot figures.

For your data, I would start with something like this:

(Import data using ‘audioread’, ‘load’, or whatever is appropriate for your file)
t = ...;                                                        % Time Vector
s - ...;                                                        % Signal Vector
L = length(s);                                                  % Signal Length (Obviously)
Ts = mean(diff(t));                                             % Sampling Interval
Fs = 1/Ts;                                                      % Sampling Frequency
Fn = Fs/2;                                                      % Nyquist Frequency
fts = fft(s)/L;                                                 % Fourier Transform
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                             % Frequency Vector
Iv = 1:length(Fv);                                              % Index Vector
figure(1)
subplot(2,1,1)
plot(Fv, abs(fts(Iv))*2)
grid
title('Fourier Transform of ‘s’')
ylabel('Amplitude')
subplot(2,1,2)
plot(Fv, angle(fts(Iv)))
grid
ylabel(Phase (rad)')
xlabel('Frequency (Hz)')

The Nyquist Frequency is the highest resolvable frequency in a sampled signal, so everything scales to it.

NOTE — This is obviously UNTESTED CODE but it should work, with appropriate modifications for your signal and the way your data are organised.

EDIT — Forgot about the decibel conversion. An anonymous function you could use for this (since your data are amplitude and not power) is:

dB = @(amplitude) 20*log10(abs(amplitude));

so you would call it as:

s_dB = dB(fts);

to get the Fourier transform of your data expressed as decibels. Note that decibels are by definition power, not amplitude.

MATLAB: FFT and smoothing of signal

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 â€”

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 â€˜sgolayfiltâ€™ 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.

Best Answer

Related Solutions

MATLAB: FFT conversion of sound pressure in the time domain.

MATLAB: FFT and smoothing of signal

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