How to plot properly a 2d fft of data?

Hi!

Ive generated a wave in a numerical model using a chirp signal and collected the responses of the model in chosen points. How can I plot properly the 2d fft of this data. The responses are in attached mat.

Here is the chirp signal:

t2=0:dt:(2e-4)-dt;

signal2 = chirp(t2,0,9.99900000000000e-05,1e6,'linear');

Is the attached image correct?

thanks in advance

Answer 1

[Star Strider]

Not entirely. The posted image is the plot of the two-sided Fourier transform after using the fftshift function. The result is that the frequency axis is not correct. (Note that a 2D fft (fft2) is usually applied to images and similarly-constructed matrices. The 1D fft is correct here.)

Try this:

D = load('matlab.mat');
mat = D.mat;

t = 0:numel(mat)-1;                                         % Time Vector (Units: Time Units)
Ts = mean(diff(t));                                         % Sampling Time Interval
Fs = 1/Ts;                                                  % Sampling Frequency
Fn = Fs/2;                                                  % Nyquist Frequency
L = numel(t);                                               % Signal Length
FTmat = fft(mat)/L;                                         % Fourier Transform
Fv1 = linspace(0, 1, fix(L/2)+1)*Fn;                       % Frequency Vector - One-Sided Fourier Transform (Units: Cycles/Time Unit)
Iv = 1:numel(Fv1);                                           % Index Vector


figure
plot(Fv1, abs(FTmat(Iv))*2)
grid
title('One-sided Fourier Transform')
xlabel('Frequency')
ylabel('Amplitude')

Fv2 = linspace(-Fn, +Fn, L);                               % Frequency Vector - Two-Sided Fourier Transform (Units: Cycles/Time Unit)

figure
plot(Fv2, fftshift(abs(FTmat)))
grid
title('Two-Sided Fourier Transform')
xlabel('Frequency')
ylabel('Amplitude')

producing:

[mm99]

Thank you! It's very helpful!

[Star Strider]

As always, my pleasure!

[mm99]

And could you please describe what does this plot represent in comparison to this data (mat) ?

[Star Strider]

It is the discrete Fourier transform of ‘mat’, using the time vector (‘t’) that I created for it (substitute the correct time vector for ‘t’ representing the correct sampling times),. and from which I derived frequency vectors ‘Fv1’ and ‘Fv2’.

It is of course the frequency content of ‘mat’, at the discrete frequencies of the respective frequency vectors.

[mm99]

Thank you for such detailed information!

[Star Strider]

As always, my pleasure!