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midterm2_w09 - Carleton University Department of Systems...

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sys-4405, winter 2009, midterm2 page 1 of 4 Carleton University Department of Systems and Computer Engineering SYSC-4405: Introduction to Digital Signal processing Winter Semester 2009 Midterm 2 March 17, 2009 Duration: 60 minutes. ______________________________________________________________________________ Answer five of the following questions Question 1 Determine the signal x(n) if its z-transform is given by: with a region of convergence Question 2 Use the z-transform to determine the convolution (as a function of the time index n) of the follow- ing two sequences: and Question 3 An LTI system has the property that when the input is , and all initial conditions are zeros, the output is given by . a) Determine the transfer function of the system. b) Indicate whether this system is causal and stable. Give a brief justification for your answer. Question 4 Cosider the system shown below: X z ( ) 1.5 z 1 1 1 2 -- z 1 1 2 z 1 ( ) ------------------------------------------------- = 1 2 -- z 2 x 1 n ( ) 1 1 1 1 , , , { } = x 2 n ( ) 1 1 1 , , { } = x n ( ) u n ( ) = y n ( ) 1 3 4 -- ⎝ ⎠ ⎛ ⎞ n u n ( ) = z 2 z 2 y n ( ) 1 4 -- x n ( ) z 2 means two sample delay
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