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I am preparing for an exam.

I found this signal I want to inverse transform using the Fourier transform:

enter image description here

The problem is that when I try using the general formula for inverse Fourier transform I get stuck by the infinities. I tried using the properties but nothing can be done.

I hope you have a way of tackling this.

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    \$\begingroup\$ kindly, show what you have attempted so far and where you need help \$\endgroup\$
    – emre iris
    Jun 23, 2020 at 19:47
  • \$\begingroup\$ Have you considered the properties of the FT? \$\endgroup\$
    – Chu
    Jun 23, 2020 at 20:04
  • \$\begingroup\$ I have forgotten most of Fourier transform or inverse transform, but shouldn't a frequency domain function be symmetrical, so that complex values can cancel each other during an inverse transform when reconstructing the signal back into time domain. What am I missing here? \$\endgroup\$
    – eliu
    Jun 23, 2020 at 20:40

1 Answer 1

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The problem is that when I try using the general formula for inverse Fourier transform I get stuck by the infinities.

The reason for this is that a cosine function has infinite energy, and therefore its Fourier transform is not a well defined function. Instead, one usually uses the Fourier series for periodic functions, since that integral will converge.

However, by convention, you can define the FT of cosine using the delta "function". See:

https://dsp.stackexchange.com/questions/11554/deriving-the-fourier-transform-of-cosine-and-sine

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