# HW7_S - HW 7 1. Consider the discrete system ECE 3704 Due...

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DKL:4/21/10 HW 7 1/5 HW 7 ECE 3704 Due 4-22-10 1. Consider the discrete system y ( n ) = h ( n k ) x ( k ) k = −∞ ; h ( n ) = 0.5 n = 1 1 n = 0 0.2 n = 1 0 otherwise (a) (5) Is this system IIR or FIR? Explain. Solution System is FIR since h ( n ) is a finite sequence. (b) (5) Find the z -transform transfer function using the definition of the z -transform. Solution Z h ( n ) { } = h ( n ) z n n = −∞ = 0.5 z + 1 + 0.2 z 1 (c) (5) Draw the pole zero diagram. Solution H ( z ) = 0.5 z + 1 + 0.2 z 1 [ ] z z = 0.5 z 2 + z + 0.2 z = 0.5( z + 1.77)( z + 0.23) z (d) (5) Is this system BIBO stable? Explain. Solution Yes, since the system is FIR.

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DKL:4/21/10 HW 7 2/5 (e) (5) Does the DTFT transfer function exist? Why? If so, find it. Solution Yes, since the system BIBO stable H ( z ) z = e j Ω = 0.5 z 2 + z + 0.2 z z = e j Ω = 0.5 e j 2 Ω + e j Ω + 0.2 e j Ω (f) (5) Find the difference equation for this system. Solution
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## This note was uploaded on 02/07/2011 for the course ECE 3704 taught by Professor Odenaal during the Spring '08 term at Virginia Tech.

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HW7_S - HW 7 1. Consider the discrete system ECE 3704 Due...

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