ECE 3240, Discrete Time Signals & Systems, Spring 2009
Problem Set # 4: convolution sum properties & tables, DT LTI system issues
Chapter 2 Problem Topics:
2.52-55 (using convolution sum properites);
2.56-68 (DT LTI system issues)
Homework # 4 (Do by Fri. Feb. 13):
•Chapter 2, Problem 52.
•Chapter 2, Problem 53.
•Chapter 2, Problem 54. Consider the input x[n] = 3nu[−n−1] + 1
3n
u[n] a DT
LTI system with impulse response h[n] = 1
4n
u[n+ 3].
1. Determine y[n] = x[n]∗h[n] without using the distributivity property of convo-
lution.
2. Determine y[n] = x[n]∗h[n] using the distributivity property of convolution.
•Chapter 2, Problem 55. Consider the cascade of two DT LTI subsystems, where the 1-
st subsystem has impulse response h1[n] = sin(8n) and the 2-nd has impulse response
h2[n] = anu[n] where |a|<1. Consider input x[n] = δ[n]−aδ[n−1] to the 1-st
subsystem. Determine y[n], the output of the 2-nd subsystem. Use of the associativity
and commutativity properties of the convolution sum can greatly simplify the solution
to this problem.
•Chapter 2, Problem 57.
•Chapter 2, Problem 58.
•Chapter 2, Problem 60.
•Chapter 2, Problem 63.
•Chapter 2, Problem 65.
•Chapter 2, Problem 69.
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