ECE111_2006SPRING_EXAM2__[0]

ECE111_2006SPRING_EXAM2__[0] - The Cooper Union Department...

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f The Cooper Union Department of Electrical Engineering ECElll Signal Processing & Systems Analysis Exam II March 31, 2006 60 min. Closed book, closed notes. No calculators. SHOW ALL WORK!! 1. [10 pts.] Find the transfer function of the system shown in Figure 1. Your answer must be explicit, but does not have to be simplifud. 2. [12 pts.] Use the method of partial fractions to find the inverse Laplace transform of: H 8 _ 8 2 + 8+ 1 ( ) - (8+3)(8+2) 3. [12 Use the method 7tial :~ti:~ t: :: ::~e = Z-1f~~ (, )py, (z) - (2z + 1) (3z - 2) ~_"\\ ~ [12 t:PGS ibly complex-v: lued) discrete-time signal x [n] has Fourier t;ansform U (DTFT (5 (w - 7f /3) 20' - 7f /4 1 Determine x [n] by evaluating the inverse Fourier transform--tn~alj in oWer worQs, write the integral explicitly and then evaluate it; you may not use integration by parts, or invoke "general pro erties" of the Fourier transform. X L ~ ') -;:;. L G [12 pts.] Given the following diffurence equation: Ii\."'" - ~ y (n) = 2x - x (n - + 3x (n - 2) - O.2y (n - + O.3y (n - + OAy (n - 3) (a) Write the transfer function H (z) as a ratio in positive powers of z (i.e., no Z-l allowed!).

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This note was uploaded on 02/27/2012 for the course CHEMISTRY/ CH/ECE/PH/ taught by Professor Faculty during the Spring '08 term at Cooper Union.

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ECE111_2006SPRING_EXAM2__[0] - The Cooper Union Department...

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