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Engineering and Tech / Signals and Systems 2 / Chapter 10 / Problem 10.34

Signals and Systems | 2nd Edition | ISBN: 9780138147570 | Authors: Alan V. Oppenheim, Alan S. Willsky, with S. Hamid

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A causal LTI system is described by the difference equation y[n] = y[n- 1] + y[n- 2] +

Chapter 10, Problem 10.34

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QUESTION:

A causal LTI system is described by the difference equation y[n] = y[n- 1] + y[n- 2] + x[n- 1]. 805 (a) Find the system function H(z) = Y(z)/X(z) for this system. Plot the poles and zeros of H(z) and indicate the region of convergence. (b) Find the unit sample response of the system. (c) You should have found the system to be unstable. Find a stable (noncausal) unit sample response that satisfies the difference equation.

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QUESTION:

A causal LTI system is described by the difference equation y[n] = y[n- 1] + y[n- 2] + x[n- 1]. 805 (a) Find the system function H(z) = Y(z)/X(z) for this system. Plot the poles and zeros of H(z) and indicate the region of convergence. (b) Find the unit sample response of the system. (c) You should have found the system to be unstable. Find a stable (noncausal) unit sample response that satisfies the difference equation.

ANSWER:

Step 1 of 8

(a) Calculating the -transform of the given equation,

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