ecen314-fall11-hw5

ecen314-fall11-hw5 - ECEN 314: Signals and Systems, Fall 11...

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Homework #5 Homework Assignment #5 Due date – Oct. 27, 2011 (Thu), 3:55PM in class. Problem 1. Fourier Series Representation (8 points) Find the Fourier series coefficients of the following continuous-time signals. [4 pt] (a) x ( t ) = e - t for - 1 < t < 1 and periodic with T = 2 . [4 pt] (b) x ( t ) = ± sin πt, 0 t 2 0 , 2 < t 4 , and periodic with T = 4 Problem 2. Fourier Series Representation (10 points) Consider the following continuous-time signals whose fundamental period is T = 1 / 2 . x ( t ) = cos(4 πt ) ,y ( t ) = sin(4 πt ) ,z ( t ) = x ( t ) y ( t ) [2 pt] (a) Find the Fourier series coefficients of x ( t ) . [2 pt] (b) Find the Fourier series coefficients of y ( t ) . [3 pt] (c) Find the Fourier series coefficients of z ( t ) . (Use the results in (a) and (b) along with the multipli- cation property of continuous-time Fourier series coefficients.) [3 pt] (d) Find the Fourier series coefficients of z ( t ) through direct expansion of
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ecen314-fall11-hw5 - ECEN 314: Signals and Systems, Fall 11...

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