Question

Which among the following is a LTI system?

(a) dy(t)/dt+ty(t)=x(t)

(b) y(t)=x(t)cosπt

(c) y(n)=x(n)+nx(n-1)

(d) y(n)=x^3 (n+1)

The question was asked during an interview.

This intriguing question originated from System Classification and Properties topic in portion Signals and Systems Basics of Signals and Systems

Answer 1

Right answer is (d) y(n)=x^3 (n+1)

Explanation: A system is said to be linear time invariant (LTI) if the input-output characteristics do not change with time.

 This expression has a coefficient which is a function of time. ∴ the system is time variant.

 Output when input is delayed by T, y(t,T)=x(t-T)cosπt

If the output is delayed by T, y(t-T)=x(t-T)cosπ(t-T)

Clearly, both expressions are not equal ∴ The system is time variant.

 Output when input is delayed by N, y(n,N)=x(n-N)+nx(n-1-N)

If the output is delayed by N,  y(n-N)=x(n-N)+(n-N)x(n-1-N)

Clearly, both expressions are not equal ∴ The system is time variant.

 Output when input is delayed by N, y(n,N)=x^3 (n+1-N)

If the output is delayed by N,  y(n-N)= x^3 (n+1-N)

Clearly, both expressions are equal. ∴ The system is time invariant.