Determine the nature of the system: y(t)= tÂ² x(t-1)

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

Linear, time variant

Linear, time invariant

Non-linear, time variant

Non-linear, time invariant

Correct Answer : Option (A) : Linear, time variant

Explanation : For input x1(t): y₁ (t)= t² x₁ (t-1)
For input x2(t): y₂ (t)= t² x₂ (t-1)
⇒ ay₁ (t)+by₂ (t)= t² [x₁ (t-1)+ bx₂ (t-1)] Equation 1
For input x3(t): y₃ (t)= t² x₃ (t-1) = t² [ax₁ (t-1)+ bx₂ (t-1)] Equation 2
∴ The system is linear.
For time invariancy: Shift in input:
⇒y(t,T)= t² x(t-1-T)
Shift in output: y(t- T)= (t-T)² x(t-1-T)
âˆµ The shift in output is not equal to the shift in input, therefore, the system is time variant.

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