# ps11 - BZT is deﬁned as follows F z = ∞ X k =-∞ f k...

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Michigan State University Department of Electrical and Computer Engineering ECE 366 INTRODUCTION TO SIGNAL PROCESSING Problem Set 11 Spring 2011 Issued: Friday, April 8, 2011 Due: NONE 1. Classify the following impulse responses of DT LTI systems in terms of BIBO stability, causality, and dynamic (or static). (a) h 1 [ k ] = δ [ k ] (b) h 2 [ k ] = sin( π 2 k + π 4 ) (c) h 3 [ k ] = 2 k u [ k ] 2. In this problem, you will better appreciate why we choose to use the unilateral z-transform (UZT) rather than the bilateral z-transform (BZT) in this course. The
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Unformatted text preview: BZT is deﬁned as follows: F ( z ) = ∞ X k =-∞ f [ k ] z-k . Compute the BZT of f [ k ] = a k u [ k ] and f [ k ] =-a k u [-k-1] and include the region of convergence in each case. Also, what is the UZT for each of these discrete-time signals? 3. Using only the fact that γ k u [ k ] ⇔ z/ ( z-γ ) and properties of the ZT, ﬁnd the ZT for the following signals: (a) k 2 γ k u [ k ] (b) k 3 u [ k ] (c) a k ( u [ k ]-u [ k-m ]) (d) k e-2 k u [ k-m ]...
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