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Inverse Fourier transform

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Find the inverse Fourier transform of each of the following Fourier transforms:

X(x) = jw

The answer I have is

x[n] = (-1)^n / n (for n not equal to zero)
0 (for n = 0)

I don't know how to get there.

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Solution Summary

This shows how to find a given inverse Fourier transform.

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Find the inverse Fourier transform of each of the following Fourier ...

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