Week 4 Assignment: Discrete-time Fourier Transform

Week 4 assignment

Assignment 3: Discrete-time Fourier Transform

Note: You may use Matlab to solve the problems where necessary

All questions carry equal points

1. Find the DTFT of the sequence .

2. Determine the DTFT of x[n] = 2nαnu[n], with |α| < 1. Hint: use the differentiation rule in the time domain.

3. If , what is its DTFT?

4. Find the IDTFT of . Hint: use the differentiation rule in the frequency domain.

5. The transfer function of an LTI discrete-time system is given by . Calculate its response to an input using DTFT.

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