Multiplication by t

Multiplication by t of-course will not leave a periodic signal periodic. But what we can do is, multiply by t in one period

, and then consider a periodic extension. i.e: x(t) is periodic with period T, we see what the Fourier series coefficients of y(t),

defined as follows is:

   in      and    

Let       

                   otherwise

Then

Note the k^th Fourier series co-efficient of x(t) is 

Similarly, let

Therefore, k^th Fourier series coefficient of

This idea is not of much use without knowledge of