# HW1_S - HW 1 ECE 3704 Due 1 Consider the system whose...

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DKL:2/9/10 HW 1 1/3 HW 1 ECE 3704 Due 2-9-10 1. Consider the system whose transfer function is Y ( s ) X ( s ) = H ( s ) = s 1 ( s + 2)( s + 8) (a) (5) Sketch the pole zero diagram. (b) (5) Find the differential equation that corresponds to this system. (c) (5) Is the system BIBO stable? Why? (d) (10) Find the step and impulse response of this system by partial fraction expansion and the Laplace transform. (e) (10) Plot the step response using MATLAB. Use the lsim command. (See the MATLAB discussions at the end of Lindner: Sec 10.1.) Note: For all MATLAB assignments, include your code and the requested graphs. Solution (a) (b) Y ( s ) X ( s ) = H ( s ) = s 1 ( s + 2)( s + 8) s 2 + 10 s + 16 ( ) Y ( s ) = ( s 1) X ( s )  y + 10 y + 16 y = x x

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DKL:2/9/10 HW 1 2/3 (c) Since two poles, -2 and -8, are located in open LHP, the system is BIBO stable. (d) The step response is Y s ( s ) = H ( s ) 1 s = s 1 s ( s + 2)( s + 8) = A s + B s + 2 + C s + 8 = 1 16
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HW1_S - HW 1 ECE 3704 Due 1 Consider the system whose...

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