114_1_sol_midterm_2010_Part1

114_1_sol_midterm_2010_Part1 - EE114 Introduction to Speech...

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Unformatted text preview: EE114 Introduction to Speech and Image Processing Winter Quarter, 2010 Midterm Exam Solutions 1. (30 points) Signal processing foundations a) (7 points) Assume that ( 29 x n and ( 29 h n are discrete, aperiodic signals specified as follows: x(n) = [1 3 4 1] h(n) = [1 2 1] As is customary, the underbar indicates the location of the origin. Find ( 29 y n , where ( 29 ( 29 ( 29 * y n x n h n = Answer: y n ( 29 = h n- m ( 29 x m ( 29 m =- y ( 29 = h- m ( 29 x m ( 29 = 1 ( 29 m = - 1 ( 29 = 1 y 1 ( 29 = h 1- m ( 29 x m ( 29 = 2 ( 29 m = - 1 ( 29 + 3 ( 29 1 ( 29 = 5 y 2 ( 29 = h 2- m ( 29 x m ( 29 = 1 ( 29 m =- 1 ( 29 + 2 ( 29 3 ( 29 + 1 ( 29 4 ( 29 = 11 y 3 ( 29 = h 3- m ( 29 x m ( 29 = 1 ( 29 m = - 3 ( 29 + 2 ( 29 4 ( 29 + 1 ( 29 1 ( 29 = 12 y 4 ( 29 = h 4- m ( 29 x m ( 29 = 1 ( 29 m =- 4 ( 29 + 1 ( 29 2 ( 29 = 6 y 5 ( 29 = h 5- m ( 29 x m ( 29 = 1 ( 29 m = - 1 ( 29 = 1 Therefore, y n ( 29 = 1 , 5, 11, 12, 6, 1 b) (15 points) Consider a discrete sequence x n ( 29 and its DTFT X ( 29 : x n ( 29 X ( 29 Now consider the discrete sequence ( 29 ( 29 y n nx n = . Denote the DTFT of y n ( 29 by ( 29 Y ....
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114_1_sol_midterm_2010_Part1 - EE114 Introduction to Speech...

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