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# Hwk4f06 - = 2 c 5 = 5 j c-3 =-2 and c-5 =-5 j All other...

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ECE 3337 Homework 4 Fall 2006 Due: October 23 (Jansen), October 24 (Kalatsky), 2006 1. Find the Fourier series of x ( t ) on the given interval (a) x 1 ( t ) = - exp( j 10 πt ) · sin(5 πt + π/ 3) (b) x 2 ( t ) = exp -| t | , over the interval (-3,3). (c) x 3 ( t ) periodic with period 3 and x 3 ( t ) = exp( - t ) , (d) x 4 ( t ) = | 2 cos(8 πt - π/ 3) | . 2. Find the signal x ( t ) for which the Fourier coefficients are c k = ( - 1 . 5) k for all k ( k integer). 3. A signal h ( t ), with period 2 sec has the following non-zero Fourier series coefficients: c 0 = -
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Unformatted text preview: = 2, c 5 = 5 j , c-3 =-2 and c-5 =-5 j . All other Fourier coeﬃcients are zero. (a) Determine the average value of the signal. (b) Determine the total power of the signal. (c) Sketch the phase spectrum. (d) Determine whether the signal is complex or real. (e) Find an expression for x ( t ) * h ( t ) when x ( t ) = 2 sin(8 πt + π/ 4). (f) Repeat Problem 3e for x ( t ) = 2 exp(6 πt ). 1...
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