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EE313 HW_11 TTH16190 Fall 2010

EE313 HW_11 TTH16190 Fall 2010 - (a The zero-input response...

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The University of Texas at Austin Department of Electrical and Computer Engineering EE 313, TTH, 16190, Fall 2010 Assignment No. 11, Due Tuesday, November 30, 2010. 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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Prob. (1) Suppose the input-output relationship of a particular LTI DT system is described by the following difference equation: y{n+2] - (1/2)y[n+1] + (1/16)y[n] = x[n] The initial conditions are y[0] = 1, y[1] = 3/4. The input x[n] is given by x[n] = (1/3) n u[n] Using z-transforms, calculate each of the following: (a)
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Unformatted text preview: (a) The zero-input response as a function of time. (b) The zero-state response as a function of time. (c) The total response as a function of time. Prob. (2) For the LTI system described in Prob. (1) (a) Calculate the system transfer function H[z] , using z-transforms. (b) Calculate the system impulse response, h[n], by calculating the inverse z- transform of H[n]. Prob. (3) For the LTI system described in Prob. (1), calculate the following in the time domain (i.e., no z-transforms are to be used) (a) Zero-input response (via characteristic equation, etc.) (b) Zero-state response using y[n] = x[n] * h[n]. (c) Add your results from (a) and (b) to get the total response. (d) Compare your time domain results for (a), (b), and (c) in this problem with the corresponding results obtained using z-transforms in Prob. (1)....
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