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A causal discrete-time system is described by the following difference equation: 20 marks y[n] = – 1 4 y[n – 2] + x[n], n = 0 where x[n] and y[n] denote the input and output signals, respectively. The initial conditions (IC) are given by y[-1] = 0 and y[-2] = -4. (a) Using the one-sided z-transform, determine the so-called zero-input response of this system, denoted yzi[n] for n = 0, resulting from the given IC when x[n] = 0. (b) Using a similar approach, determine the zero-state response of this system, denoted yzs[n] for n = 0, obtained when the input signal is a unit step, i.e. x[n] = u[n], and the IC are set to 0. (c) Determine the total response of the system, i.e. y[n] for n = 0 when y Document Preview:

McGILL UNIVERSITY FINAL EXAMINATIONFaculty of Engineering APRIL 2010DISCRETE TIME SIGNAL PROCESSINGECSE 412 (Winter 2010)Examiner: Prof. Beno^ t Champagne Co-Examiner: Prof. Peter KabalSignature: Signature:Date: April 19, 2010Time: 14:00 to 17:00INSTRUCTIONS: This is a CLOSED BOOK examination. Faculty standard calculator permitted ONLY. This examination paper consists of 5 printed pages, including: a cover page, 5questions, and useful formulas in appendix. Ensure that you have a complete examination before starting. Answer ALL questions. Use one or more Answer Booklets for your solutions. DO NOT return this examination paper.April 19, 2010 ECSE 412 1/51. A causal discrete-time system is described by the following dierence equation: 20 marks1y[n] =