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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 [ n5] 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 [n1] the output is y [ n ] = 14 ± 1 4 ¶ n u [ n ]14 ± 1 2 ¶ n u [n1] (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 diﬀerence equation that is satisﬁed 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 diﬀerence equation found in part (c). 2...
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 Fall '09
 Digital Signal Processing, Signal Processing, LTI system theory, Time Fourier Transform, Department of Electrical and Computer Engineering ECE

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