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How far does the memory of the given system y[n]=1/2{x[n]+ x[n-1]} extend into past?

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How far does the memory of the given system y[n]=1/2{x[n]+ x[n-1]} extend into past?

(a) Two time units

(b) One time unit

(c) Three time units

(d) Not predictable

The question was posed to me during an interview for a job.

This intriguing question originated from Properties of Systems in division Signals and Systems Basics of Signals and Systems

1 Answer

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by (42.1k points)
The correct option is (b) One time unit

The explanation: The given memory system extends into past by one time unit. It is determined by the term x [n-1].

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