Module 3 : Sampling and Reconstruction
Lecture 28 : Discrete time Fourier transform and its Properties
 

Time and Frequency Scaling:

Time reversal  

Let us find the DTFT of x[-n]

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Time expansion:

It is very difficult for us to define x[an] when a is not an integer. However if a is an integer other than 1 or -1 then the original signal is not just speeded up. Since n can take only integer values, the resulting signal consists of samples of x[n] at an.

If k is a positive integer, and we define the signal

then

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