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EE313 HW_6 TTH16190 Fall 2010

EE313 HW_6 TTH16190 Fall 2010 - must express the solution...

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The University of Texas at Austin Department of Electrical and Computer Engineering EE 313, TTH, 16190, Fall 2010 Assignment No. 6, Due Tuesday, September 12, 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 ********************************************************************************* Suppose the input-output relationship of a particular LTI DT system is described by the following difference equation: a 2 y[n+2] + a 1 y[n+1] + a 0 y[n] = b 1 x[n+1] + b 0 x[n] For problems (1), (2), and (3) find the zero-input response y 0 [n] for the values given for the “a” coefficients and initial conditions.

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Unformatted text preview: must express the solution in the “standard form” given in class, with β and θ expressed in radians, in order to receive credit. (1) a 2 = 1, a 1 = 18, a = 81; y[-2] = 12/81, y[-1] = -2. (2) a 2 = 1, a 1 = -2, a = 4; y[-2] = -2 +√3, y{-1] =2(2 + √3). (3) a 2 = 1, a 1 = 14, a = 48; y[-2] = 7/24, y[-1] = -2. (4) Using direct integration (no calculators), solve for c ( t ) = x 1 (t)* x 2 ( t ), where the asterisk denotes convolution and 3( 6) 1 2 ( ) 5 ( 6) ( ) ( 9) t x t e u t x t u t Probs. (5) and (6) are continued on the next page. Please note that an “Introduction to MATLAB” is provided in Appendix B of Roberts’ textbook. (5) Plot the following functions using MATLAB: a. u[n-5] b. rect 8 [n] c. 10 ramp[n/2] d. cos[ 2πn/10] ( 6) Compute and plot the even and odd parts of the following using MATLAB . : a. rect 5 [n+2] b. comb 3 [n-1]...
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