ecen314_pm - is as large as possible at t = 2 Problem 3(CT...

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ECEN 314: Signals and Systems Practice Midterm October 5, 2011 Problem 1 (DT LTI System): Consider a serial interconnection of two DT LTI systems as shown below. y[n] x[n] h [n] 1 h [n] 2 The unit impulse responses of the LTI systems are given by h 1 [ n ] = δ [ n ] + δ [ n - 1] and h 2 [ n ] = 2 n u [ n ] respectively, where u [ n ] is the unit step function. Let the input x [ n ] = δ [ n ] - 2 δ [ n - 1]. Determine and sketch the corresponding output y [ n ]. Problem 2 (CT LTI System): Let h ( t ) be a CT signal shown below (the signal is zero outside the region shown). h(t) 1 -1 0 2 1 t (a) Let x ( t ) = u ( t ) - u ( t - 1) where u ( t ) is the unit step function. Determine and sketch x ( t ) * h ( t ). 1
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(b) Determine and sketch a choice of x ( t ) such that all three conditions below are met simul- taneously: (i) x ( t ) = 0 for t < 0; (ii) | x ( t ) | ≤ 1 for t 0; and (iii) x ( t ) * h ( t
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Unformatted text preview: ) is as large as possible at t = 2. Problem 3 (CT Fourier Series): Consider a periodic CT signal x ( t ) with fundamental period T = 1. x ( t ) is deFned over one period as x ( t ) = t for 0 ≤ t < 1. (a) Sketch x ( t ) for-1 ≤ t < 1. ±ind the ±ourier series coe²cients of x ( t ). (b) The even part of x ( t ) is deFned as EV{ x ( t ) } = x ( t )+ x (-t ) 2 . Sketch EV{ x ( t ) } for-1 ≤ t < 1. ±ind the ±ourier series coe²cients of EV{ x ( t ) } . (c) The odd part of x ( t ) is deFned as OD{ x ( t ) } = x ( t )-x (-t ) 2 . Sketch OD{ x ( t ) } for-1 ≤ t < 1. ±ind the ±ourier series coe²cients of OD{ x ( t ) } . 2...
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ecen314_pm - is as large as possible at t = 2 Problem 3(CT...

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