Question

Which one of the following systems is causal?

(a) y(t)=x(t)+x(t-3)+x(t^2)

(b) y(n)=x(n+2)

(c) y(t)=x(t-1)+x(t-2)

(d) y(n)=x(2n^2)

The question was asked in an online interview.

My question is from System Classification and Properties topic in chapter Signals and Systems Basics of Signals and Systems

Answer 1

The correct choice is (c) y(t)=x(t-1)+x(t-2)

Best explanation: A causal system is one in which the output depends on the present or past values of the input, not future. If it depends on future values then it is non-causal. For y(t)=x(t)+x(t-3)+x(t^2), y(n)=x(n+2), and y(n)=x(2n^2), the output depends on future values i.e., x (t^2), x (n + 2) and x (2n^2) respectively. Whereas in y(t)=x(t-1)+x(t-2), the output y(t) depends on past values only i.e., x(t – 1) and x(t – 2).