HW_1_Sol - HW 1 ECE 3704 Due 2-3-07 1. Consider the system...

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HW 1 1/4 HW 1 ECE 3704 Due 2-3-07 1. Consider the system whose transfer function is Y ( s ) X ( s ) = H ( s ) = s ! 3 ( s + 1)( s + 4) (a) (5) Sketch the pole zero diagram. (b) (5) Find the differential equation that corresponds to this system. (c) (5) Does the Fourier transform transfer function of this system exist? Why? If so, find it. (d) (5) Is the system BIBO stable? Why? (e) (10) Find the step and impulse response of this system by Laplace transform. (f) (10) Plot the step and impulse responses using MATLAB. Use the lsim command. (See the MATLAB discussions at the end of Lindner:Sec 10.1.) Solution (a) pole-zero diagram (b) differential equation Y ( s ) X ( s ) = H ( s ) = s ! 3 ( s + 1)( s + 4) = s ! 3 s 2 + 5 s + 4 s 2 + 5 s + 4 ( ) Y ( s ) = s ! 3 ( ) X ( s ) !! y + 5 ! y + 4 y = ! x ! 3 x (c) The Fourier transform exists because the poles are in the open LHP. Y
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HW_1_Sol - HW 1 ECE 3704 Due 2-3-07 1. Consider the system...

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