Transform of Periodic Sequences
Here we study the DTFT of periodic sequences. We'll start by looking
at the Fourier Series expansion, analogous to what we did in
continuous time. Then we will derive the same result using a
different approach that will lead us into the Discrete Fourier
Transform for finite length sequences.
Recall that for continuous time periodic signals, we found the
Fourier transform by first doing a Fourier series expansion
Discrete-time periodic signals can also be
described by a Fourier Series expansion:
First, recall that
. Then since
), the 's are periodic with
period and only terms are needed in the sum.