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

Electronics and Communication Engineering (ECE) : Signals and Systems - Quiz(MCQ)

Causal, Linear

Causal, Non-linear

Non-Causal, Non-linear

Non-causal, Linear

Correct Answer : Option (D) : Non-causal, Linear

Explanation : 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.

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