how to find the right frequency axis when we take the Fourier transform of a function?
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I want to know how to find the correct frequency axis when I am taking the fourier transfor. To make it clear, we know that for sinc function, we have the below relationship between the lenght of the sinc function and its fourier (the rect function):
based on this fact, each time I tried different frequency axix and then finally I find the correct one. But, actually I still do not know how to find the correct axis. This was a simple function that I already knew about the lenght of the function and its transforemed but for other functions I do not have any idea about the correct frequency axis.
Any help will be appreciated
Paul on 22 Jun 2022
Edited: Paul on 23 Jun 2022
By default, the frequency variable for fourier in the Symbolic Math Toolbox is in rad/sec.
Also, Matlab definition of sinc in the SMT is sinc(x) = sin(pi*x)/(pi*x).
So with the example in the question we have:
syms t omega f T real
s(t,T) = sinc(2*t/T);
S_omega(omega,T) = simplify(fourier(s(t,T),t,omega));
Now, if we want the CTFT expressed in Hz
S_f(f,T) = simplify(S_omega(2*sym(pi)*f,T))
Now make some plots for T = 2
As expected and consistent with the plot in the Question, the mainlobe of s(t) has a span of T the CTFT spans -1/T to 1/T.