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I am studying electrical engineering and have an assignment which I have been working on for couple weeks, but can't solve.

I have a discontinuous function as shown below and applied a FFT on it, which can be seen on the right.

On the bottom right corner is the inverse FFT plot in order to visualize the Gibb's effect, but I am not able to see it.

Why isn't the Gibb's effect showing up in this case?

Graph

Program

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  • \$\begingroup\$ The FFT/IFFT, for the same number of points, is supposed to perfectly reconstruct the signal. If you want the Gibbs phenomenon, use a greater number of points (which will give you the leakage), or plot the sum of odd harmonics generating a square wave, as seen in the Wikipedia page. Also, what you have there is quite the tapered signal, which means that there is a triangle involved, which, in turn, means the harmonics will be more attenuated than the ones of a square wave. \$\endgroup\$ Commented Jan 4, 2021 at 9:54
  • \$\begingroup\$ Thanks concerned citizen. So by using a greater number of points you mean more points in calculating the FFT and therefore less points for the IFFT? \$\endgroup\$
    – Verman
    Commented Jan 4, 2021 at 10:11

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You need to restrict the number of harmonics used when reconstructing the original signal else, it'll look just like the original. The Gibb's effect is all about not using the full spectrum. Wiki explains this well. Here's a reconstructed square wave using 125 harmonics: -

enter image description here

And here's the same but only using 5 harmonics: -

enter image description here

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