hw7 - ASE 330M Linear System Analysis Unique Number: 12495,...

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ASE 330M Linear System Analysis Unique Number: 12495, Spring 2006 Homework #7 Date given: April 27, 2006 Date Due: May 4, 2006 1. An LTI system has a step response ( e - t cos 2 t ) u ( t ). Determine an ordinary diﬀerential equa- tion representation for this system. 2. An LTI system at zero initial conditions is subject to an input signal x ( t ) = [sin(2 t )] u ( t ). The resulting output is designated by y ( t ) = [4 e - t + 2sin(2 t ) - 4cos(2 t )] u ( t ). (a) Determine an ordinary diﬀerential equation representation for this system. (b) Determine whether the system is BIBO stable. (c) Depending on your answer in part (b), evaluate (if possible) the frequency response function H ( j Ω) for this system. Further, obtain expressions for the magnitude and argument (phase angle) of the frequency response function. (d) Analytically determine the frequency Ω = Ω max at which the magnitude of the frequency response function has a maximum value. Also calculate the magnitude of the frequency

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This note was uploaded on 09/25/2011 for the course ASE 18510 taught by Professor Jeannefalcon during the Spring '10 term at University of Texas.

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hw7 - ASE 330M Linear System Analysis Unique Number: 12495,...

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