assignment 4_New - Signals and Systems (EENG 320)...

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Signals and Systems (EENG 320) Assignment (4) 1- Determine the Fourier series representation for the following signals: i. periodic with period 2 and ) ( t x 1 1 - for ) ( < < = t e t x t ii. Each illustrated in figures (1)-(3). ) ( t x Figure 1 t x(t) 1 -2 1 2 3 -3 -2 -1 -4 -5 4 5 6 t x(t) Figure 2 1 -1 -2 -1 -5 -3 -6 -4 4 5 2 1 -7 -8 3 6 7 8 1
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t x(t) Figure 3 1 -1 -2 -1 -5 -3 -6 -4 4 5 2 1 3 6 7 8 2 2- Let be a periodic signal with fundamental period T and Fourier series coefficients a . Derive the Fourier series coefficients of each of the following signals in terms of : ) ( t x k k a ) ( 0 t t x t x + + i. ) ( 0 t ii. )} ( { t x Ev iii. )} ( { t x e iv. 2 2 ) ( dt t x d 3- Suppose we are given the following facts about a signal : ) ( t x i. is a real even periodic signal, with period T=4, and has Fourier series coefficients a . ) ( t x k ii. 1 0 > = k for a k iii. 5 . 0 ) ( 4 1 4 0 2 = dt t x iv. = 9 5 0 ) ( 4 1 dt t x Determine the signal . ) ( t x 4- A discrete-time periodic signal [] x n is real valued and has a fundamental period N=5. the nonzero Fourier series coefficients for x n are */ 6* 4 3 02 2 4 2, 2 , j j aa ae
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This note was uploaded on 03/13/2012 for the course EENG 320 taught by Professor Sherifabdelaseem during the Spring '10 term at American University in Cairo.

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assignment 4_New - Signals and Systems (EENG 320)...

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