Question

Which of the following systems is time invariant?

(a) y(t) = x(2t) + x(t)

(b) y(t) = x(t) + x(1-t)

(c) y(t) = -x(t) + x(1-t)

(d) y(t) = x(t) + x(t-1)

I had been asked this question in an internship interview.

My question is taken from Properties of Systems topic in portion Signals and Systems Basics of Signals and Systems

Answer 1

Correct option is (d) y(t) = x(t) + x(t-1)

The best explanation: In each of a, b and c there is a negative sign of t involved, which means a backward shift of t-0 in time, would mean a forward shift in each of them. However, only in d, the backward shift will remain as backward, and undiminished.