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**Unformatted text preview: **transform. Specify the region of convergence for X ( z ), Y ( z ) and H ( z ). (a) x [ n ] = 1 2 u [-n ] and h [ n ] = ( 1 2 ) n u [ n ] (b) x [ n ] = u [ n-5] and h [ n ] = 2cos( n ) u [ n ] Problem 4 (20 points) When the input to a LTI system is x [ n ] = 1 4 n u [ n ]-2 n u [-n-1] the output is y [ n ] = 14 1 4 n u [ n ]-14 1 2 n u [-n-1] (a) Find the system function H ( z ) = Y ( z ) X ( z ) of the system. Determine the poles and zeros of H ( z ) and indicate the region of convergence. (b) Find the impulse response h [ n ] of the system. (c) Write a dierence equation that is satised by the given input and output. Is the system causal ? Comment if this is consistent with the ROC in part (a). (d) Draw a system block diagram corresponding to the dierence equation found in part (c). 2...

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