I have question of FFT(fast fourier transform)

I have a question fft of time domain and frequency domain. I know FFT show the signal how works at frequency domain.

when we use FFT. we declare Ts(time scale) = 1/Fs(Frequency sampling).

why we did it?

If there`s no relations. what will happen?

Fs = 1e6; Ts = 1/Fs; t = 0 : Ts : 2e-2; There is no reason to do that?

Thanks.

Answer 1

[Christoph F.]

A Fourier transform decomposes a time-domain signal into sinusoidal components. The frequencies of the sinusoidal components are chosen so that n whole oscillations fit in the time Ts covered by the time-domain signal.

Therefore, the frequency resolution of the Fourier transform is equal to 1/Ts. If, for example, Ts is 4 seconds, then the lowest frequency at which one whole oscillation will fit in Ts is 0.25 Hz. At 0.5 Hz, two oscillations will fit in 4s, at 0.75 Hz three, at 1 Hz four, and so on.

If the frequency axis of the Fourier transform is not scaled correctly, then the plot will not reflect the frequency components of the signal correctly.

This appears to be more of a general mathematical question than a MatLab-specific question. The mathemactical background of the Fourier transform is described in much more detail in appropriate literature.

Answer 2

[Jayanta Deb]

If you don't calculate the frequency scale correctly then while plotting the FFT's out come you wont be able to plot it properly, if you can calculate the frequency scale as an X axis then you will be able to see the peak of the exact frequency(s) you are looking for.