# sp09hw09 - ω | F-ω = | F-ω | e j ∠ F-ω = | F ω | e j...

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HW 9 Solutions: Kudeki and Munson book, Chapter 7, Problems: 1, 2, 3, 4, 5, 7, 8 7.1

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7.2
7.3

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7.4 So F(ω) is absolutely integrable. Also, F(ω) is plottable so it satisfies the Dirichlet conditions.
7.5

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7.6 Δ( t ) = ( 1 - 2 | t | | t | ≤ 1 / 2 0 else 2 ( t/ 5) = ( 5(1 - 2 | t/ 5 | ) 2 | t/ 5 | ≤ 1 / 2 0 else = ( 5(1 - 2 / 5 | t | ) 2 | t | ≤ 5 / 2 0 else F (0) = Z -∞ 2 ( t/ 5)d t = Z 5 / 2 - 5 / 2 5(1 - 2 / 5 | t | ) 2 d t = 2 Z 5 / 2 0 5(1 - 2 / 5 t ) 2 d t = 10 Z 5 / 2 0 1 - 4 / 5 t + 4 / 25 t 2 d t = 10 ± t - 2 / 5 t 2 + 4 / 75 t 3 ² 5 / 2 0 = 10[5 / 2 - 2 / 5 · 25 / 4 + 4 / 75 · 125 / 8] = 25 / 3 1

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7.7 a F ( - ω ) = Z -∞ f ( t )e - j ( - ω ) t d t = Z -∞ f ( t )e jωt d t = Z -∞ f ( t ) ± e - jωt ² * d t = ³Z -∞ f ( t )e - jωt d t ´ * = F * ( ω ) b | F ( - ω ) | = F ( - ω ) F * ( - ω ) = F * ( ω ) F * ( - ω ) = F * ( ω ) F ( w ) = | F
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Unformatted text preview: ( ω ) | F (-ω ) = | F (-ω ) | e j ∠ F (-ω ) = | F ( ω ) | e j ∠ F (-ω ) F * ( ω ) = | F ( ω ) | e-j ∠ F ( ω ) By part (a), F (-ω ) = F * ( ω ). Therefore, | F ( ω ) | e j ∠ F (-ω ) = | F ( ω ) | e-j ∠ F ( ω ) e j ∠ F (-ω ) = e-j ∠ F ( ω ) j ∠ F (-ω ) =-j ∠ F ( ω ) ∠ F (-ω ) =-∠ F ( ω ) 1 7.8...
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## This note was uploaded on 04/09/2010 for the course ECE 210 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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sp09hw09 - ω | F-ω = | F-ω | e j ∠ F-ω = | F ω | e j...

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