20112ee113_1_Hw3

20112ee113_1_Hw3 - a) ±or what value of the index n does...

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EE113: Digital Signal Processing Spring 2011 Prof. Mihaela van der Schaar (Instructor) Homework #3 This homework consists of two parts. Part 1 Solve the following problems from the electronic versions of the chapters of An Undergraduate Course on Discrete-Time Signal Processing by A.H. Sayed Problem 6.3. Problem 6.5 (using both graphical and analytical evaluation). Problem 7.1. Problem 7.3. Problem 7.4. Part 2 Solve the following additional problems. Problem A. Let y ( n ) = x ( n ) * h ( n ) where x ( n ) = f ( n )[ u ( n - n 1 ) - u ( n - n 2 )] and h ( n ) = g ( n )[ u ( n - n 3 ) - u ( n - n 4 )] where f ( n ) and g ( n ) are arbitrary functions with positive values ( f ( n ) ,g ( n ) > 0 for all n ) and n 1 < n 2 and n 3 < n 4 . Therefore, x ( n ) and h ( n ) are pulse-like signals of Fnite duration n x = n 2 - n 1 and n h = n 4 - n 3 , respectively.
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Unformatted text preview: a) ±or what value of the index n does the Frst non-zero output element y ( n ) occur? b) ±or what value of the index n does the last non-zero output element y ( n ) occur? c) What is the duration n y of the output sequence y ( n ) in terms of n x and n h ? Problem B. Let y [ n ] be the sequence obtained by a linear convolution of two causal Fnite-length sequences h [ n ] and x [ n ]. Determine x [ n ] for the following pair of y [ n ] and h [ n ]. The Frst sample of in each sequence is at time index n = 0. { y [ n ] } = { 2 , 1 , 2 , 6 , , 17 , 12 } , { h [ n ] } = { 2 ,-3 , 2 , 3 } 1...
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This note was uploaded on 10/07/2011 for the course EE 113 taught by Professor Walker during the Spring '08 term at UCLA.

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