Module 2 : Signals in Frequency Domain
Lecture 19 : Periodic Convolution and Auto-correlation
Fourier Transform of

Say x(t) is periodic with period T1 and h(t) is periodic with period T2 with T1 / T2 = m / n (where m and n are integers).

Thus m T2 = n T1 = T is a common period for the two.

We can expand x(t) and h(t) into Fourier Series with fundamental frequency :

                                      

If one compares the Fourier co-efficients in these expansions with those in the expansions with the original fundamental frequencies, i.e:

                                     , we find:

         

                                                                                                                                                                                                            

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