Question

Examine whether the system described by the following input/output relationships are (i) linear or nonlinear, (ii) time variant or time invariant, (iii) memoryless or with memory, and (iv) causal or noncausal.

(a) y₁(t) = x₂(t) + 5x(t)

Answer 1

The input/output relationship y₁(t) = x₂(t) + 5x(t) can be examined to determine its linearity, time variance, memory, and causality.

Step-by-step explanation:

The input/output relationship y₁(t) = x₂(t) + 5x(t) can be examined to determine whether it is linear or nonlinear, time variant or time invariant, memoryless or with memory, and causal or noncausal.

(i) To determine if the system is linear or nonlinear, we need to check if it satisfies the properties of linearity. A system is linear if it satisfies two properties: additivity and homogeneity.

(ii) To determine if the system is time variant or time invariant, we need to check if it changes over time. A system is time variant if its characteristics change with time, and time invariant if its characteristics remain constant over time.

(iii) To determine if the system is memoryless or with memory, we need to check if its output only depends on the current input or if it depends on past inputs as well.

(iv) To determine if the system is causal or noncausal, we need to check if its output depends only on the current and past inputs, or if it depends on future inputs as well.