20105ee102_1_hw5

# 20105ee102_1_hw5 - 2 π 6 n π 4 3 Suppose the following...

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1 EE102 Systems and Signals Fall Quarter 2010 Jin Hyung Lee Homework #5 Due: Wednesday, November 3, 2010 at 5 PM. 1. Prove the Discrete Time Fourier Series of the Following Signal is 1 N sin[2 πk ( n 0 + 1 / 2) /N ] sin( πk/N ) 0 N n 0 -n 0 -N ... ... ... ... 1 2. Find the Discrete Time Fourier Series of the Following Signals: (a) 0 12 -12 ... ... ... ... 1 8 2 (b) 0 3 -3 ... ... 1 2 3

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2 (c) x [ n ] = 1 + cos( 2 π 3 n ) + sin(
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Unformatted text preview: 2 π 6 n + π 4 ) 3. Suppose the following information is given: (a) x[n] is real and odd signal. (b) x[n] has period N = 8 and Fourier coefﬁcients a k . (c) a 9 = 3 (d) 1 8 7 ∑ n =0 | x [ n ] | 2 = 18 . Show that x [ n ] = Acos ( Bn + C ) , and ﬁnd out the value of A , B and C ....
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20105ee102_1_hw5 - 2 π 6 n π 4 3 Suppose the following...

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