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EE313 HW_5 TTH16190 Fall 2010

EE313 HW_5 TTH16190 Fall 2010 - (t 18y(t = b 1 x(1(t b x(t...

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The University of Texas at Austin Department of Electrical and Computer Engineering EE 313, TTH, 16190, Fall 2010 Assignment No. 5, Due Tuesday, October 5, 2010 Please note all homework assignments will be posted on Blackboard. It is your responsibility to monitor Blackboard for homework assignments. Course handouts will likewise be available on Blackboard. Please include the following information on the first-page of each assignment: (1) Your name (printed legibly), (2) course number EE 313 , (3) Assignment Number , and (4) Due Date . Thank you. Please staple your homework pages together. Page numbers refer to the course textbook by Roberts In view of the fact that classes were cancelled for Tuesday, September 28th, I have abbreviated this HW assignment. Prob. (1) Suppose the input-output relationship of a particular LTI system is described by the following differential equation: y (2) (t) + 6y (1)
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Unformatted text preview: (t) + 18y(t) = b 1 x (1) (t) + b x(t) Find the zero-input response y (t) , subject to the following initial conditions y(0) = -8, y (1) (0) = 48. . If the eigenvalues are complex, you must express the solution in the “standard form” given in class in order to receive credit. In Problems (2), (3), (4), and (5) below, evaluate the indicated convolutions. Express your answer in mathematical form and also carefully sketch (i.e., indicate all important coordinates) for the result c(t) . The asterisk denotes convolution. Prob. (2) c(t) = tri(t/3) * δ(t) Prob. (3) c(t) = tri(4t) * δ(t - 5) Prob. (4) c(t) = rect(t/6) * δ(2(t - 5)) Prob. (5) c(t) = rect(4t) * comb(t) Evaluate the indicated convolutions in Prob. (6) and (7). Express your result in mathematical form. Prob. (6) c(t) = u(t) * u(t) , where u(t ) is the unit step function. Prob. (7) c(t) = e λt u(t) * e λt u(t)...
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