solutions_midterm2_w09

solutions_midterm2_w09 - Carleton University Department of...

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sys-4405, winter 2009, midterm2 page 1 of 7 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 solution 1 with a ROC The first factor above has a ROC while the second factor has a ROC . Therefore the inverse trasform must be: 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 Solution 2 Therefore Xz () 1.5 z 1 1 1 2 -- z 1 ⎝⎠ ⎛⎞ 12 z 1 ------------------------------------------------- = 1 2 z 2 ≤≤ 1.5 z 1 1 1 2 z 1 z 1 1 z 1 ------------------- 1 1 1 2 z 1 == 1 2 z 2 z 2 1 2 z xn 2 n un –1 1 2 n = x 1 n 1111 ,,, {} = x 2 n 111 ,, = Y 1 z X 1 z X 2 z 1 z 1 z 2 z 3 +++ 1 z 1 z 2 ++ z 1 3 z 2 3 z 3 2 z 4 z 5 +++++ = yn δ n 2 δ n 1 3 δ n 2 3 δ n 3 2 δ n 4 δ n 5 =
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sys-4405, winter 2009, midterm2 page 2 of 7 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.
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solutions_midterm2_w09 - Carleton University Department of...

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