12Spring_hw08_solns

# 12Spring_hw08_solns - ECE210 - Spring 2012 - Homework 08...

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ECE210 - Spring 2012 - Homework 08 Solutions Kudeki and Munson, Problems 6.1(c) and 6.4 1. Problem 6.1(c) from text Solution: 2. Problem 6.4 from text 1

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Solution: 3. (a) 3 1 is a rational number, so the signal is periodic. The fundamental frequency ω 0 is 1, so the period is 2 π . (b) 7 4 is a rational number, so the signal is periodic. The DC term (or constant) does not aﬀect the periodicity of the signal. The fundamental frequency ω 0 is 1, so the period is 2 π . (c) π 3 is not a rational number, so the signal is not periodic. (d) 2 π π = 2 1 is a rational number, so the signal is periodic. The fundamental frequency ω 0 is π , so the period is 2 . (e) 2 2 is not a rational number, so the signal is not periodic. 2
(f) sin 3 ( x ) = 1 2 (1 - cos(2 x )) sin( x ) = 1 2 sin( x ) - 1 2 cos(2 x ) sin( x ) = 1 2 sin( x ) - 1 4 (sin(3 x ) - sin( x )) = 3 4 sin( x ) - 1 4 sin(3 x ) Since 3 1 is a rational number, the signal is periodic. The fundamental frequency ω 0 is 1, so the period is 2 π

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## This note was uploaded on 03/28/2012 for the course ECE ece210 taught by Professor Ece during the Spring '10 term at University of Illinois, Urbana Champaign.

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12Spring_hw08_solns - ECE210 - Spring 2012 - Homework 08...

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