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114_1_midterm_2010

114_1_midterm_2010 - EE114 Introduction to Speech and Image...

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Unformatted text preview: EE114 Introduction to Speech and Image Processing Winter Quarter, 2010 Midterm Exam 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 = b) (15 points) Consider a discrete sequence x n ( 29 and its DTFT X ϖ ( 29 : x n ( 29 ← → X ϖ ( 29 Now consider the discrete sequence ( 29 ( 29 y n nx n = . Denote the DTFT of y n ( 29 by ( 29 Y ϖ . Express (in the most simplified form possible) ( 29 Y ϖ in terms of ( 29 X ϖ . c) (8 points) Consider the following statement: A signal of the form ( 29 ( 29 1 cos 2 f t f t π θ = + , where 1 and f θ are constants, subjected to ideal sampling at a sampling frequency of 1 2 f , can be reconstructed with no error. Is this statement always true, and if not, under what conditions will it be true?...
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114_1_midterm_2010 - EE114 Introduction to Speech and Image...

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