Week 5 Assignment: Discrete Fourier Transform
Question # 00818116
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Updated on: 01/25/2022 04:31 AM Due on: 01/25/2022
Week 5 assignment
Assignment 4: Discrete Fourier Transform
Note: You may use Matlab to solve the problems where necessary
All questions carry equal points
1. If the convolution , where and are both periodic with period N, show that is also periodic with period N.
2. Determine the 5-point DFT of .
3. Show that the circular convolution is a) commutative, and b) associative. You may show this by an example using Matlab.
4. Let {x[n]} = {-3, 2, -1, 4} and {h[n]} = {1, 3, 2, -2} be two length-4 sequences for 0 ≤ n ≤ 3. Compute the circular convolution of x[n] and h[n] using the matrix equation.
5. Let x[n] and X[k] be the N-point DFT pairs. Find the sequence whose DFT is given by , where m1 and m2 are positive integers less than N.
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Solution: Week 5 Assignment: Discrete Fourier Transform