Question

The system \( y(t) = x(2t) + 3 \) is:

• A. Linear and Time-invariant
• B. Causal and Linear
• C. Nonlinear and Time-variant
• D. Linear

Hint:

A system is nonlinear if there is an additive constant or if the system operation does not satisfy superposition. Time scaling (e.g., \( x(2t) \)) makes the system time-variant.

Answer 1

The Correct Option is C

To determine the properties of the system, let's check its linearity and time invariance. 1. Linearity: A system is linear if it satisfies both the principle of superposition and scaling. In this case, the system involves a time scaling factor (the argument \( 2t \)) and an additive constant (3). The constant term makes the system nonlinear. 2. Time-invariance: A system is time-invariant if shifting the input signal by a certain time results in a corresponding shift in the output. Here, the time scaling (i.e., \( 2t \)) means the system is time-variant. Therefore, the system is nonlinear and time-variant.