Assignment # 4 Digital Signal Processing – Spring 2012
(Prepared By: Dr. M. Arif Khan)
Submission Date: Monday, 30th April, 2012 (Before Class) – There will be a quiz after this
assignment as well.
---------------------------------------------------------------------------------------------------------------------
Question # 1: Perform the circular convolution of the following. Consider the first element of
each sequence at index value zero.
( ) * + ( ) * +
Answer: ( ) * + with zero index at the first element.
Question # 2: Determine the mod-4 and mod-3 reduction of the length-8 signal vector.
* +T
Answer:
, -
, -
Question#3: Compute the 4-point DFT of the length-8 signal of the signal
* +T in two ways.
(a) Working with the full wrapped vector and
(b) Computing DFT of its mod-4 reduction.
Answer: Hint use for part (a) ( )
, answer for both should
be same and is , - .
Question#4: Let * +. Compute 4-point DFT of using the definition in matrix
form. Recomputed it by first reducing modulo 4 and then computing the 4-DFT of the result.
Finally, compute the 4-point IDFT of the result and verify that you recover the mod-4 wrapped
version of .
Question#5: Compute the length-4 circular convolution of the two signals , - and
, - in two ways:
a) By computing their linear convolution and then, reducing the result mod-4.
b) By first reducing h and x mod-4, computing the linear convolution of the reduced signal,
and reducing the result mod-4.
Question#6: Find the DFS expression of the sequence .
/ .
Answer:
Docsity.com
