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Assignment3_w10

Assignment3_w10 - Carleton University Department of Systems...

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1 of 2 Carleton University Department of Systems and Computer Engineering SYSC-4405: Digital Signal processing Winter Semester 2010 Assignment # 3 Date Due: March 5, 2010, before 1:00 p.m. ______________________________________________________________________________ Problem 1 Determine the z-transform of the following signals and sketch the corresponding pole-zero pat- tern a) , a is real and N is a positive integer. b) Problem 2 Compute the convolution of the following signals by means of the z-transform and Problem 3 a) Determine the causal signal having the z-transform b) Determine, in closed form, the causal signal whose z-transform is partially check your results by computing and using an alternative method. Problem 4 Compute the zero-state response for the following system when the input is Is the system stable? Problem 5 We want to design a causal discrete-time LTI system with the property that if the input is x n ( ) a n 2 π n N --------- sin u n ( ) u n N ( ) [ ] = x n ( ) 1 2 -- n 2 1 3 -- ⎝ ⎠ ⎛ ⎞ n 1 u n 1 ( ) = x 1 n ( ) 1 3 -- ⎝ ⎠ ⎛ ⎞ n u n ( ) = x 2 n ( ) u n ( ) = X z ( ) 1 1 1 2 -- z 1 1 z 1 ( ) 2 ------------------------------------------------
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