ecen314-fall11-hw7

ecen314-fall11-hw7 - ECEN 314 Signals and Systems Fall...

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Unformatted text preview: ECEN 314: Signals and Systems, Fall ‘11 Homework #7 Homework Assignment #7 Due date – Dec. 7, 2011 (Wed), noon @ Zachry 237F Problem 1. Fourier Transform (14 points) Find the Fourier transform X ( e jω ) of the discrete-time signal x [ n ] described below: [2 pt] (a) x [ n ] = u [ n ]- u [ n- 5] [3 pt] (b) x [ n ] = 3 n u [- n ] [3 pt] (c) x [ n ] = ( 1 3 ) n u [ n + 3] [3 pt] (d) x [ n ] = ( 1 2 ) n sin( π 2 n ) u [ n ] [3 pt] (e) x [ n ] = ( 1 2 ) | n | cos( π 2 n ) Problem 2. Inverse Fourier Transform (15 points) Find the discrete-time signal x [ n ] that corresponds to the Fourier transform X ( e jω ) shown below: [3 pt] (a) X ( e jω ) = u ( | ω | - π 3 ) , | ω | ≤ π [3 pt] (b) X ( e jω ) = u ( | ω | - π 3 )- u ( | ω | - 2 π 3 ) , | ω | ≤ π [3 pt] (c) X ( e jω ) = ω, ≤ ω < π ω + π,- π ≤ ω < [3 pt] (d) X ( e jω ) = 1 6- 5 e- jω + e- 2 jω [3 pt] (e) X ( e jω ) = 1- 5 e- jω + 6 e- 2 jω 6- 5 e- jω + e- 2 jω Problem 3. Multirate System (18 points)...
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ecen314-fall11-hw7 - ECEN 314 Signals and Systems Fall...

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