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hw8 - ASE 330M Linear System Analysis Unique Number 12880...

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ASE 330M Linear System Analysis Unique Number: 12880, Spring 2007 Homework #8 Date Given: May 1, 2007 Due Date: May 9, 2007 at 10.00am 1. An LTI system at zero initial conditions is subject to an input signal x ( t ) = te - 3 t u ( t ) . The resulting output is designated by y ( t ) = e - 2 t (sin 2 t ) u ( t ) . (a) Determine whether the system is BIBO stable. (b) 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. (c) Analytically determine the frequency Ω = Ω max at which the magnitude of the fre- quency response function has a maximum value. Also calculate the magnitude of the frequency response function at frequency Ω max . (d) Use MATLAB commands impulse and step to plot the impulse and step responses for this system on the range 0 t 30 . Submit both the plots and your source code. 2. An LTI system has transfer function H ( s ) = s 2 + 2 s ( s 2 + 3 s + 2)( s 2 + s - 2) (a) Determine whether the system is BIBO stable.
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