single sided amplitude fourier spectrum

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Muhsin 2017-10-12

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评论： Star Strider 2017-10-18

A00.txt

Hello all, I am new user that trying to learn coding. I have an acceleration-time history with a time-step of 0.01 sec. The total duration is 14 sec. I would like to get a single-sided fourier spectrum of it. Is there any packed code for it? Any kind of help is appreciated. The attached file contains the data. Thank you.

Muhsin

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Star Strider 2017-10-12

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/360889-single-sided-amplitude-fourier-spectrum#answer_285445

编辑：Star Strider 2017-10-12

在 MATLAB Online 中打开

See the documentation for fft (link).

The Code —

D = dlmread('Muhsin A00.txt', '\t', 1,0);
t = D(:,1);                                             % Time (s)
a = D(:,2);                                             % Acceleration (g)
L = length(t);
Ts = t(2)-t(1);                                         % Sampling Interval (sec)
Fs = 1/Ts;                                              % Sampling Frequency (Hz)
Fn = Fs/2;                                              % Nyquist Frequency (Hz)
FTa = fft(a)/L;                                         % Fourier Transform (Scaled)
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                     % Frequency Vector
Iv = 1:length(Fv);                                      % Index Vector
figure(1)
plot(Fv, abs(FTa(Iv))*2)                                % One-Sided Amplitude Plot
xlabel('Frequency (Hz)')
ylabel('Amplitude (g)')
grid

EDIT — Changed ‘Ts’ calculation to accommodate ‘t(1)=0.01’ and ‘t(end)=0’.

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Star Strider 2017-10-12

在 MATLAB Online 中打开

My pleasure.

The difference is that your data are zero-padded for some reason. I used them as you posted them.

Try this (limiting the data to only the non-zero values of ‘t’):

D = dlmread('Muhsin A00.txt', '\t', 1,0);
t = D(:,1);                                             % Time (s)
a = D(:,2);                                             % Acceleration (g)
t_end = find(t == 0, 1, 'first');                       % Last Non-Zero ‘t’
idx = 1:t_end-1;                                        % Index For Non-Zero ‘t’
L = length(t(idx));
Ts = t(2)-t(1);                                         % Sampling Interval (sec)
Fs = 1/Ts;                                              % Sampling Frequency (Hz)
Fn = Fs/2;                                              % Nyquist Frequency (Hz)
FTa = fft(a(idx))/L;                                    % Fourier Transform (Scaled)
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                     % Frequency Vector
Iv = 1:length(Fv);                                      % Index Vector
figure(1)
plot(Fv, abs(FTa(Iv))*2)                                % One-Sided Amplitude Plot
xlabel('Frequency (Hz)')
ylabel('Amplitude (g)')
grid

I could not determine if you wanted to retain the zeros or eliminate them. I eliminated them in this code. Note that it also affects the frequency vector. If you want to zero-pad your signal to increase the frequency resolution, use the second ‘NFFT’ argument to the fft function to do that in MATLAB:

D = dlmread('Muhsin A00.txt', '\t', 1,0);
t = D(:,1);                                             % Time (s)
a = D(:,2);                                             % Acceleration (g)
t_end = find(t == 0, 1, 'first');                       % Last Non-Zero ‘t’
idx = 1:t_end-1;                                        % Index For Non-Zero ‘t’
L = length(t(idx));
Ts = t(2)-t(1);                                         % Sampling Interval (sec)
Fs = 1/Ts;                                              % Sampling Frequency (Hz)
Fn = Fs/2;                                              % Nyquist Frequency (Hz)
NFFT = 2^nextpow2(t_end-1);
FTa = fft(a(idx), NFFT)/L;                              % Fourier Transform (Scaled)
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                     % Frequency Vector
Iv = 1:length(Fv);                                      % Index Vector
figure(1)
plot(Fv, abs(FTa(Iv))*2)                                % One-Sided Amplitude Plot
xlabel('Frequency (Hz)')
ylabel('Amplitude (g)')
grid

This is the correct way to calculate and plot the Fourier transform of your signal. The Nyquist frequency is 50 Hz, the maximum resolvable frequency for your sampling frequency of 100 Hz.