EL 611 HW_ZT

# EL 611 HW_ZT - Suppose , the input to the system, is a unit...

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EL611 3 1) An LTI system is to have the transfer function 2 2 ) 2 / 1 )( 3 ( ) 4 / 15 2 / 15 2 ( ) ( + + = z z z z z z H . a) Sketch the pole-zero diagram for ) ( z H . b) If the system is to implemented by stable recursions, find an equation that can be used to implement it. c) Find ) ( n h . 2) When the input to an LTI system is the corresponding output is a) Find the system function of the system. Plot the pole(s) and zero(s) of and indicate the region of convergence. b) Find the impulse response of the system. c) Write a difference equation that is satisfied by the given input and output. d) Is the system stable? Is it causal? 3) Consider an LTI system with input and output that satisfies the difference equation 4) A causal LTI system has the system function a) Find the impulse response system of the system, . b) Find the output of this system, , for the input u[n-1]. 5) Consider an LTI system that is stable and for which , the z-transform of the input response, is given by

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Unformatted text preview: Suppose , the input to the system, is a unit step sequence. a) Find the output by evaluating the discrete convolution of and . b) Find the output by computing the inverse z-transform of . 6) Consider an LTI system that is stable and for which , the z-transform of the input response, is given by Suppose , the input to the system, is a unit step sequence. a) Find the output by evaluating the discrete convolution of and . b) Find the output by computing the inverse z-transform of . 7) If the input to an LTI system is , the output is a) Find , the z-transform of the system impulse response, and plot its pole-zero diagram. b) Find the impulse response . c) Is the system stable? d) Is the system causal? 8) Consider a stable linear time-invariant system. The z-transform of the impulse response is Suppose , the input to the system, is 2 . Determine at ....
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## EL 611 HW_ZT - Suppose , the input to the system, is a unit...

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