ecen444-fall09-hw3

# ecen444-fall09-hw3 - k = 1 2 3 Plot the output signal y k 1...

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ECEN 444: Digital Signal Processing, Fall‘09 Homework #3 Homework Assignment #3 Due date – Oct. 2, 2009 (Fri), 12:40PM in class. Problem 1. Understanding convolution (5 points) Solve problem P2.20 in the textbook. Problem 2. Interconnected LTI systems (10 points) Solve problem P2.35 in the textbook. Problem 3. Analysis of a simple IIR system (10 points) Solve problem P2.47 in the textbook. Problem 4. Impulse response of a recursive system (10 points) Solve problem P2.53 in the textbook. Problem 5. MATLAB (15 points) Consider the following input signals x 1 ( n ) ,x 2 ( n ) ,x 3 ( n ) and the systems h 1 ( n ) ,h 2 ( n ) : x 1 ( n ) = cos ± πn 6 ² u ( n ) x 2 ( n ) = cos ± πn 2 ² u ( n ) x 3 ( n ) = cos ³ 5 πn 6 ´ u ( n ) h 1 ( n ) = 1 2 δ ( n ) + 1 2 δ ( n - 1) h 2 ( n ) = δ ( n ) - δ ( n - 1)

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(a) Use MATLAB to plot the input signals x 1 ( n ) , x 2 ( n ) , and x 3 ( n ) . * Hint: >> help plot (b) Use MATLAB to compute y k 1 ( n ) = x k ( n ) * h 1 ( n ) for all input signals (
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Unformatted text preview: k = 1 , 2 , 3 ). Plot the output signal y k 1 ( n ) obtained from passing the input x k ( n ) through the LTI system h 1 ( n ) . * Hint: >> help conv (c) Discuss the results in (b). Do you see what the system h 1 ( n ) does to the input signals? (d) Use MATLAB to compute y k 2 ( n ) = x k ( n ) * h 2 ( n ) for all input signals ( k = 1 , 2 , 3 ). Plot the output signal y k 2 ( n ) obtained from passing the input x k ( n ) through the LTI system h 2 ( n ) . (e) Discuss the results in (d). Do you see what the system h 2 ( n ) does to the input signals? * Note: You only need to plot the ﬁrst 100 samples of all the input and output signals....
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ecen444-fall09-hw3 - k = 1 2 3 Plot the output signal y k 1...

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