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A#22 - Assignment#22 ECSE-2410 Signals Systems Spring 2007...

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Assignment #22 ECSE-2410 Signals & Systems - Spring 2007 Wed 05/02/07 1(14). Find X ( z ), the z -transform (in closed form) of the following repeating sequences: (a)(8). x [ n ] = {1 , 0, -1, 2, 1, 0, -1, 2, 1, 0, -1, 2,…}. (b)(6). { } ... , 3 , 2 , 1 , 3 , 2 , 1 , 3 , 2 , 1 , 0 , 0 ] [ = n x . 2(10). The model for a particular system is unknown, but we do have measurements available at the output. Suppose we input x [ n ]= u [ n ] and observe that ,...} , , , , 0 { ] [ 16 15 8 7 4 3 2 1 = n y . Find H ( z ), the transfer function for this system. 3(18). Find the closed form analytic expressions for the inverse z -transforms of the following. Use tables and properties. (a)(6). 2 1 3 ) ( = z z z X a . (b)(6). 2 1 ) ( + + = z z z X b . (c)(6). 2 1 2 1 2 2 ) ( + = z z z z X c . 4(20). The difference equation, ( ) ] [ ] 1 [ 1 ] [ n x n y n y α α = , represents a digital filter, where the parameter, α , determines the “cutoff” frequency of the filter (i.e., the bandwidth). (a)(3). Find the transfer function, , of this filter. ) ( z H (b)(2). Plot the poles and zeros of in the z-plane. ) ( z H (c)(8). Find the unit step response, . Note that ] [ n y α is still an unspecified parameter. (d)(7). Use MATLAB and the “filter” function (type, “help filter”) to plot (i.e., stem(y) )
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