MT(483)S09

MT(483)S09 - EE 483 Introduction to Digital Signal...

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1 EE 483 – Introduction to Digital Signal Processing Spring 2009 Midterm Examination – February 25, 2009 1. (10 Points) Consider the following finite-length sequences: (i) h [ n ], ± M ² n ² N , and (ii) g [ n ], K ± n ± N , where M , N and K are positive integers with K < N . Define (a) y 1 [ n ] = h [ n ]O * h [ n ], (b) y 2 [ n ] = h [ n ]O * g [ n ], (c) y 3 [ n ] = g [ n ]O * g [ n ]. What are the lengths of each of the above convolved sequences? What are the ranges of the index n for which each of the above convolved sequences are defined? 2. (15 Points) Let X ( e j ± ) denote the DTFT of a discrete-time sequence x [ n ]. (a) Express the DTFT of ( ± 1) n x [ n ] in terms of X ( e j ) . (b) Express ( n = ±² ² ³ ± 1) n x [ n ] in terms of X ( e j ) . (c) Let Y ( e j ) = X ( e j ) + X ( e j ( ² ³ ) ). Show that Y ( e j ) depends only on the even-indexed samples x [2 m ] and not on the odd-indexed samples x [2 m + 1]. 3.
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MT(483)S09 - EE 483 Introduction to Digital Signal...

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