Question

The continuous time system described by the equation y(t) = x(t^2) comes under the category of ____________

(a) Causal, linear and time varying

(b) Causal, non-linear and time varying

(c) Non-causal, non-linear and time invariant

(d) Non-causal, linear and time variant

I had been asked this question during an interview.

My doubt stems from Fourier Analysis in division Fourier Analysis on Complex Spaces of Signals and Systems

Answer 1

The correct option is (d) Non-causal, linear and time variant

Explanation: Let y (t) = x (t^2). We can infer that y (t) depends on x (t^2) i.e. on future values of input if t>1. Hence, the system is non-casual.

Again, α x1(t) → y1 (t) = α x1(t^2) and β x2(t) –> y2 (t) = β x2(t^2)

Therefore α x1(t) + β x2(t) –> y (t) = α x1(t^2) + β x2(t^2) = y1 (t) + y2 (t), which implies that the system is linear.

Again, x (t) = u (t) – u (t-z) –> y (t) and X1(t) = x (t – 1) –> y1 (t).

So, we get, y1 (t) ≠ y (t –1), which implies that the system is time varying.