Lecture 28 : Discrete time Fourier transform and its Properties
Another way of representing DTFT of
a periodic discrete signal
In continuous time, the fourier transform of is an impulse at .However in discrete time ,for signal the
discrete time fourier transform is periodic in with period . The DTFT of is a train of impulses at i.e Fourier Transform can be written as :
Consider a periodic sequence x[n] with period N and with fourier series representation
Then discrete time Fourier Transform of a periodic signal x[n] with period N can be written as :
is an impulse at 
.However in discrete time ,for signal 
the
discrete time fourier transform is periodic in 
with period 
. The DTFT of 
i.e Fourier Transform can be written as :
