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Unformatted text preview: 1 EE113 Homework 5 Problem 6.7 Evaluate the convolution sum
n−1 1
3 u(−n + 2) ⋆ · u(n − 2) using both the analytical and graphical methods. Compare your results. Problem 6.9 Evaluate
n−1 1
2 1
3 · u(n) ⋆ n · u(n − 2) − u(n + 1) using the distributivity property of the convolution sum. Problem 6.23 Consider two possibly complexvalued sequences x(n) and h(n). Their crosscorrelation is the
sequence rxh (n) whose samples are deﬁned as follows:
∞ rxh (n) = x(k )h∗ (k − n)
k=−∞ (a) Verify that rxh (n) = x(n) ⋆ h (−n).
∗ (b) Use the graphical method to evaluate the correlation of the two sequences:
x(n) = {−2, 1, −1, 2} and h(n) = {0, 1, 2} Problem 6.31 A causal LTI system is described by the difference equation
y (n) = 1
y (n − 1) + x(n − 1)
4 Find its impulse response sequence. Find also the response to the input sequence shown in Fig. 6.18 using the
convolution sum method. Problem 7.9 Determine the solution of each of the following homogeneous equations with initial conditions:
(a) y (n) + 9y (n − 2) = 0, y (0) = 0, y (−1)=1.
(b) y (n) + 9y (n − 2) = 0, y (0) = 0, y (−1)=j. September 28, 2011 DRAFT 2 Problem 7.11 Find the impulseresponse sequences of the following causal LTI systems:
(a) y (n) + y (n − 1) − 5y (n − 2) = x(n).
(b) y (n) = −4y (n − 2) + x(n − 1).
(c) y (n) − 4y (n − 2) = 2x(n). Problem 7.19 Consider the relaxed and causal system
5
1
y (n) + y (n − 1) − y (n − 2) = x(n − 2)
6
6
(a) Is the system BIBO stable?
(b) Find its impulseresponse sequence.
(c) Find its response to x(n) = ( 1 )n u(n − 2).
2 Problem 7.31 Find the solution y (n) of the socalled Fibonacci difference equation
y (n) − y (n − 1) − y (n − 2) = 0
with y (−1) = 0 and y (0) = 1. September 28, 2011 DRAFT ...
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This note was uploaded on 01/24/2012 for the course EE 113 taught by Professor Walker during the Fall '08 term at UCLA.
 Fall '08
 Walker

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