Question

Determine the nature of the given system: y(t)=x(sint)

(a) Causal, Non-linear

(b) Causal, Linear

(c) Non-Causal, Non-linear

(d) Non-causal, Linear

This question was posed to me by my college director while I was bunking the class.

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

Answer 1

The correct option is (d) Non-causal, Linear

The explanation is: The system is non-causal as it gives future values for some inputs.

E.g. y (- π) = x (sin (-π)) = x (0)

For linearity, it needs to satisfy superposition principle,

⇒ y1 (t) = x1 (sint)

⇒ y2 (t) = x2 (sint)

⇒ ay1 (t) + by2 (t) = ax1 (sint) + bx1 (sint)  Equation 1

Now, y3 (t) = x3 (sint) = (ax1 + bx2)(sint) = ax1 (sint) + bx1 (sint)  Equation 2

Clearly, Equation 1 and 2 are equal, hence the system is linear.