Topic: Signals and Systems
The system $y(t) = x(2t) + 3$ is
- A. Linear and time invariant
- B. Causal and linear
- C. Non-linear and time variant
- D. Linear and memoryless
Answer: C. Non-linear and time variant
Explanation: A system is time-invariant if a delay in the input produces the same delay in the output. For $y(t) = x(2t) + 3$, delaying the input yields $x(2t - t_0) + 3$, but delaying the output yields $x(2(t - t_0)) + 3 = x(2t - 2t_0) + 3$, making it time-variant. Furthermore, the addition of the constant term $+3$ means it violates the superposition principle (specifically the zero-in, zero-out property), making it non-linear.