Question: Consider a system with input x[n] and output y[n]. The input-output relation for the system is defined by the following two properties: 1. y[n]

Consider a system with input x[n] and output y[n]. The input-output relation for the system is defined by the following two properties:

1. y[n] – ay[n – 1] = x[n],

2. y[0] = 1.

(a) Determine whether the system is time invariant.

(b) Determine whether the system is linear.

(c) Assume that the difference equation (property 1) remains the same, but the vale y[0] is specified to be zero. Does this change your answer to either Part (a) or part (b)?

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a Even though x 2 n x 1 n 1 y 2 n y 2 n 1 Hence the system is NOT TIME INVARIANT ... View full answer

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