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}\, $
