HW12f09_soln

# HW12f09_soln - GEORGIA INSTITUTE OF TECHNOLOGY ECE 2025...

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GEORGIA INSTITUTE OF TECHNOLOGY ECE 2025 SOLUTIONS Problem Set # 12 Fall 2009 Problem 12.1 (a) Since < X ( ) = 0, we get | X ( ) | = |= X ( ) | = | ω | ( u ( ω + 7 π ) - u ( ω - 7 π )). (b) See Figure 1. 7 π - 7 π 7 π | X ( ) | ω (a) | V ( ) | 66 π - 66 π - 71 π - 59 π 59 π 71 π ω (b) 7 π/ 2 Figure 1: Plots for P-12.1 The following plots are not to scale. The width of each block is 14 π (as before). | W ( ) | 51 π - 51 π ω 81 π - 81 π 7 π/ 4 15 π - 15 π Figure 2: | W ( ) | (c) See Figure 3 (next page). 1

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Z ( ) | ω - 132 π - 102 π - 30 π 30 π 102 π 132 π - 23 π - 7 π 7 π 23 π H ( ) 7 π/ 4 4 ω 7 π/ 8 Figure 3: | Z ( ) | and H (( ) Problem 12.2 (a) Nyquist frequency: ω s = 2 × 80 π = 160 π . T s = 2 π ω s = 2 π 160 π = 1 80 A T s = 80 A - 80 π 80 π ω Figure 4: Problem 12.2.a: X s ( ) (b) For ω s = 150 π : T s = 2 π ω s = 2 π 150 π = 1 75 A T s = 75 A - 80 π 80 π ω - 150 π 150 π 70 π Figure 5: Problem 12.2.b:
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## This note was uploaded on 11/24/2010 for the course ECE 2025 taught by Professor Juang during the Spring '08 term at Georgia Tech.

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HW12f09_soln - GEORGIA INSTITUTE OF TECHNOLOGY ECE 2025...

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