Example of Computation of inverse Fourier transform (CT signals)

A practice problem on CT Fourier transform

The formula of the inverse transform is:

$ x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} X(jw)e^{jwt}dw \, $

Suppose we have $ 2 \pi \delta(w - 2\pi) $ (From the 'not so easy' question in class)

Substituting that into the formula:

$ x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} 2 \pi \delta(w - 2\pi) e^{jwt}dw \, $
$ x(t) = \int_{-\infty}^{ \infty} \delta(w - 2\pi) e^{jwt}dw \, $
$ x(t) = e^{j2 \pi t}\, $

Back to Practice Problems on CT Fourier transform

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