Question

Which one of the following is an example of a system with memory?

(a) Identity System

(b) Resistor

(c) y(n)=x(n)-2x(n)

(d) Accumulator

The question was posed to me in quiz.

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

Answer 1

Right choice is (d) Accumulator

The explanation is: An identity system gives the output same as input hence it totally depends on the present state of the input. Therefore, it is memory less. Similarly, a resistor and the expression in option c are memory less systems as they depend upon the present state of the input. An accumulator sums up the values of all past and present states of input. Therefore, it is a system with memory.