We now obtain the result equivalent to the Parseval's theorem we have already seen in the context of periodic signals.

Let x(t) and y(t) be periodic with a common period T.

Applying the Convolution theorem equivalent we have just proved on we get:

Put t = 0, to get:

Compare this equation with the Parseval's theorem we had proved earlier.

If we take x = y, then T becomes the fundamental period of x and:

Note the left-hand side of the above equation is the power of x(t).

Note also that the periodic convolution of  yields a periodic signal with Fourier coefficients that are the modulus square of the coefficients of x(t).