The continuous-frequency spectrum of a signal x(1) is given byX (f)=28 (f+40) + 28 (ƒ+30)+38 (ƒ+20)+4+38 (ƒ-20) +28 (ƒ-30)+28 (-40)(a) Draw an adequately labeled sketch of the power spectral density, P, (f), of x(t).(b) What is the average power of x(t)?www.(c) The 80% power containment bandwidth of a power signal is defined as thesmallest bandwidth that contains at least 80% of the average signal power. Whatis the 80% power containment bandwidth of x(1) ?

Answered: The continuous-frequency spectrum of a…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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The continuous-frequency spectrum of a signal x(1) is given by
X (f)=28 (f+40) + 28 (ƒ+30)+38 (ƒ+20)+4
+38 (ƒ-20) +28 (ƒ-30)+28 (-40)
(a) Draw an adequately labeled sketch of the power spectral density, P, (f), of x(t).
(b) What is the average power of x(t)?
www.
(c) The 80% power containment bandwidth of a power signal is defined as the
smallest bandwidth that contains at least 80% of the average signal power. What
is the 80% power containment bandwidth of x(1) ?

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According to the question, the continuous-frequency spectrum of a signal x(t) is given by

$straight x open parentheses straight f close parentheses space equals space 2 straight delta open parentheses straight f plus 40 close parentheses space plus space 2 straight delta open parentheses straight f plus 30 close parentheses space plus space 3 straight delta open parentheses straight f plus 20 close parentheses space plus space 4 space plus space 2 straight delta open parentheses straight f minus 40 close parentheses space plus space 2 straight delta open parentheses straight f minus 30 close parentheses space plus space 3 straight delta open parentheses straight f minus 20 close parentheses semicolon$

(a) Draw an adequately labeled sketch of the power spectral density, P_x (f), of x(t).
(b) What is the average power of x(t)?
(c) The 80% power containment bandwidth of a power signal is defined as the smallest bandwidth that contains at least 80% of the average signal power. What is the 80% power containment bandwidth of x(t)?

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