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20102ee113_1_Homework4

# 20102ee113_1_Homework4 - 1 2 n u n(d n δ(e 1 n δ(f 1 n...

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Some of following problems are from the electronic versions of the chapters of An Undergraduate Course on Discrete-Time Signal Processing , by Prof. A.H. Sayed (posted on the class website): Problem 8.7 (parts 1-5, and 7-11 only) Note that in parts 1 to 5 the system is assumed to be relaxed. Problem 9.4 Problem 9.10 parts a, b, and c only. Note that the initial conditions are ( 2) 0 y - = and ( 1) 4/3 y - =- . Problem A: Determine the z-transform, including the region of convergence, for each of the following sequences: (a) ( ) ( ) 1 2 n u n (b) ( ) ( ) 1 1 2 n u n - - - (c)
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Unformatted text preview: ( ) 1 2 n u n-(d) ( ) n δ (e) ( ) 1 n δ-(f) ( ) 1 n δ + (g) ( ) ( ) ( ) [ ] 1 10 2 n u n u n--Problem B: Consider the following complex series expansion of the natural logarithm around the point 1 z = , ( ) ( ) 1 1 1 ln 1 , 1 n n n z z z n ∞ + =-+ = < ∑ Use the result to determine the sequence ( ) x n whose z-transform is given by ( ) ( ) 1 ln 1 , X z z z α α-= + > Problem C: Find the inverse z-transform of ( ) ( ) 1 50 50 1 1 2 z X z z--=-EE113 Digital Signal Processing Homework 4 Prof. Mihaela van der Schaar...
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