# Assignment3 - EE 2200 / Spring 2009: Assignment Three 1 ECE...

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EE 2200 / Spring 2009: Assignment Three 1 ECE 2200 / Spring 2009 TRANSFER FUNCTIONS ASSIGNMENT THREE 1 1. For the following discrete-time systems with input x and output y , you are to determine if they are time-invariant (or not) and if they are linear (or not). You are to ﬁrst answer these questions analytically, and then, using Matlab, construct experiments to support your answer that perform the tests shown in Figures 5- 16 and 5-17 of McClellan, Schafer, and Yoder, Signal Processing First (Pearson Prentice hall, 2003). (a) y [ n ] = x [ - n ] (b) y [ n ] = cos(2 πfn ) x [ n ] (c) y [ n ] = | x [ n ] | 2. Consider two linear and time-invariant discrete-time systems with impulse responses h 1 and h 2 . (a) If they are connected in series so that the output of the system with impulse response h 1 is the input to h 2 , the impulse response of the overall system is the convolution of h 1 and h 2 . Write a Matlab script that conﬁrms this result for h 1 = [1 , 2 , 3 , 4] and h 2 = [5 , 6] for the input x [ n ] = [7 , 8 , 9 , 10]. Conﬁrm that this result is not altered by re-ordering the cascade connection so the input x enters system h 2 and its output is the input to h 1 . (b) If they are connected in parallel so that both receive the same input and the outputs of the system with impulse response h 1 is added to the output of h 2 , the impulse response of the overall system is the sum of h 1 and h 2 . Write a Matlab script that conﬁrms this result for h 1 = [10 , 9 , 8 , 7] and h 2 = [6 , 5] for the input x [ n ] = [4 , 3 , 2 , 1]. 3. Consider the transfer function

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## This note was uploaded on 03/02/2011 for the course ECE 2200 taught by Professor Johnson during the Spring '05 term at Cornell University (Engineering School).

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Assignment3 - EE 2200 / Spring 2009: Assignment Three 1 ECE...

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