I am trying to get the Fourier transform of a sinc function but I don't know why fft() (fast Fourier transform) is not working as it works for a basic sine function.

Here is my code, the plot produced is empty:

function fourier_transform

Ts= 1/50000;
t = 0:Ts:.5-Ts;
% p = sin(40*t);
m = sin(100*t)./(100*t);

f = fft(m);
plot(t,abs(f));

end 

CodePudding user response：

m(1) is computed by sin(0)/0, which equals NaN.

NaN means "Not a Number", and indicates an error situation. Any computation you do with NaN will propagate that NaN, to warn you that there was an error somewhere along the way when computing. For example, sum(m) equals NaN. Since each output element of the FFT involves computations with each input of m, all of those output elements will be NaN as well.

Your f is all NaN, and plot will just skip the NaN points, and so produces no output.

You can fix your computation in one of two ways:

1. Avoid the division by zero by dividing by 100*t 1e-9, the very small value added will prevent a zero but otherwise not affect other results.

    m = sin(100*t)./(100*t   1e-9);
   

2. Know that m(1) involves a division by zero and fix it.

    m = sin(100*t)./(100*t);
    m(1) = 1;