20092ee102_1_S09-102-HW-7

20092ee102_1_S09-102-HW-7 - Spring 2009 Put First Letter of...

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Spring 2009: Put First Letter of LAST Name in the corner →→%% ( Otherwise Your HW Will Be LOST! ) PRINT: (LAST , Middle, First):——————————————————– EE102: SYSTEMS & SIGNALS HW: # 7 A LATE HW IS A NON-HW! Posted: May 14 Hand In To Me 1 : May 21 Attach This Sheet To Your HW (Otherwise It Will Be Lost!) 0. (i) (See Sols. below) Consider the periodic signal x ( t ) defined (over one period) as x ( t ) = 0 , t [ 1 , 0) = t, t [0 , 1) Compute X n then write down the Fourier Sine-Cosine series of x ( t ). (ii) (See Sols. below) The periodic signal of part (i) is now applied to a system S whose system function H ( s ) admits the following poles and zeroes: a simple zero at 0 , a simple pole at 1 , a double zero at 1 Moreover H (2) = 1 9 Write down the Fourier series of the corresponding output. (iii) ( UDIP: Hand in this part ) Compute the MSE when x ( t ) is ap- proximated by the finite FS denoted by x 2 ( t ): x 2 ( t ) := 2 X n = 2 X n e in π t . 1 during the break of the Thursday Lecture 1
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SOLS. (i) T = 2 ω 0 = 2 π T = π .
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