Homework_8

# Homework_8 - 1 EE113 Homework 8 Problem 12.5 Determine the...

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1 EE113 Homework 8 Problem 12.5 Determine the unilateral z -transforms of each of the following sequences and indicate their regions of convergence: (a) x ( n ) = ( n - 1) u ( n + 1) . (b) x ( n ) = (1 + n 2 α n - 2 ) u ( n + 31) . (c) x ( n ) = α | n | with α > 0 . (d) The impulse response sequence of the relaxed causal system y ( n ) - 3 4 y ( n - 1) + 1 8 y ( n - 2) = x ( n - 1) . Problem 12.21 Consider a causal system that is described by the difference equation y ( n ) = 5 6 y ( n - 1) - 1 6 y ( n - 2) + x ( n - 2) , y ( - 2) = 0 , y ( - 1) = 1 Use the unilateral z -transform to determine its complete response to the sequence x ( n ) = ( n - 1) p 1 4 P n - 2 u ( n - 1) Problem 12.25 Consider the constant-coefFcient difference equation y ( n ) - 1 6 y ( n - 1) - 1 6 y ( n - 2) = x ( n - 1) with initial conditions y ( - 2) = 0 and y ( - 1) = 6 . Use the z -transform technique to Fnd the answers to parts (a)-(c): (a) The zero-input response.

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Homework_8 - 1 EE113 Homework 8 Problem 12.5 Determine the...

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