Fourier Transform of Periodic signals.

We know the Fourier transform of the signal that assumes the value 1 identically is the dirac-delta function.

By the property of translation in the frequency domain, we get:

This is the result we will make use of in this section.

Suppose x(t) is a periodic signal with the period T, which admits a Fourier Series representation. Then,

Now since the Fourier transformation is linear, the above result can be used to obtain the Fourier Transform of the periodic signal x(t):

Therefore,