I have obtained the fourier transform of a signal with following graph

enter image description here

My question (though might be too junior for the professionals in signal processing field) is: how can we extract the period of 30 from the fourier transform mag graph?

The source code is

Fs = 1;
Ts = 1/Fs;
dt = 0:Ts:30*4-Ts;

 y1 = [
  100 ; zeros(Fs*29,1);
  100 ; zeros(Fs*29,1);
  100 ; zeros(Fs*29,1);
  100 ; zeros(Fs*29,1);

plot(dt, y1, 'r')
title('impulse happen in time series', 'fontsize', 18);

X = fft(y1);
X_mag = abs(X)
title('fourier transform mag', 'fontsize', 18);

Assuming you are in the continuous-time domain, given the periodic impulse train with a period of $T_0$

$$ x(t) = \sum_k \delta(t - k T_0)$$

then its CTFT will be another periodic impulse train in the frequency domain $$ X(\omega) = \frac{2\pi}{T_0} \sum_k \delta( \omega - k\omega_0)$$

Where the period $\omega_0$ of the frequency impulses is related to the period of the time impulses as

$$ \omega_0= \frac{2\pi}{T_0} $$

hence the time period will be given as:

$$ T_0 = \frac{2\pi}{\omega_0} $$

In your case, if $T_0 = 30$ then $\omega_0$ will be $$ \omega_0 = \frac{2\pi}{30} = \frac{\pi}{15} $$

Conversely, given the frequency period as $\frac{2\pi}{30}$ then the corresponding time period will be $T_0 = 30$.

Note that there will be errors in your computation depending on how you simulate the impulse train or CTFT.

| improve this answer | |
  • $\begingroup$ Thanks for your reply! My original intention is to extract T0 out of Fourier transform in frequency domain, it turns out given the relation of 2*Pi = T0 * W0, I come to the original question again, that is how to extract W0 in the graph. $\endgroup$ – Johnson Dec 10 '19 at 4:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.