Inverse Discrete-Time Fourier Transform

INVERSE DISCRETE-TIME FOURIER TRANSFORM

The process of finding the discrete time sequence x(n) from its frequency response X(ω) is called the inverse discrete-time Fourier transform.

Problems Based on Inverse Discrete - Time Fourier Transform

Problem 1:

Determine the signals x(n) for the given Fourier transforms:

Solution:

Problem 2:

Obtain the impulse response of the system described by

Solution:

This impulse response h(n) is given by

Problem 3:

Find the inverse Fourier transform of the following:

Solution:

The Fourier transform X(ω) in given. Then, the inverse Fourier transform of X(ω) in given by

Problem 4:

Find the inverse Fourier transform of

Solution:

We know that X(ω) = 

Comparing the above two values of X(ω), we get