Question

Determine whether the following systems are linear or non-linear, causal or non-causal, time invariant or time variant, and memoryless or with memory:

(a) y(t)=2x(t) + 3

Answer 1

The system represented by (t)=2x(t) + 3 is linear, causal, time-invariant, and memoryless.

Step-by-step explanation:

Linear: The system follows the principle of superposition, where scaling and addition properties hold true. This is evident as the output y(t) is a linear combination of the input x(t).

Causal: It's causal because the output at any given time t depends only on the present and past values of the input, not future values.

Time-invariant: The system's behavior remains constant over time; there's no dependency on when the input is applied.

Memoryless: It's memoryless as the output at any time depends solely on the input at that particular time, lacking a dependence on past or future inputs.

In summary, the system y(t)=2x(t) + 3 is linear (satisfying superposition), causal (dependent on present and past inputs), time-invariant (behavior doesn’t change with time), and memoryless (output at any time only relies on the input at that instant).

Correct Answer: Linear, Causal, Time-Invariant, Memoryless