Consider a system with input x[n] and output y[n] that satisfy the difference equation y[n] = ny[n

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Consider a system with input x[n] and output y[n] that satisfy the difference equation

y[n] = ny[n – 1] + x[n].

The system is causal and satisfies initial-rest conditions; i.e., if x[n] = 0 for n < n₀, then y[n] = 0 for n < n₀.

(a) If x[n] = δ[n], determine y[n] for all n.

(b) Is the system linear? Justify your answer.

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Discrete Time Signal Processing

ISBN: 978-0137549207

2nd Edition

Authors: Alan V. Oppenheim, Rolan W. Schafer

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Question Posted: May 26, 2011 02:55 AM

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Consider a system with input x[n] and output y[n] that satisfy the difference equation y[n] = ny[n

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The difference equation Since the system is causal and satisfies initialrest conditions we may re...View the full answer

Discrete Time Signal Processing

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