The LTI Criteria

A system is linear and time-invariant if it meets two criteria:

Linearity: If input x₁(t) produces output y₁(t) and input x₂(t) produces output y₂(t), the linear combination a₁x₁(t) + a₂x₂(t) generates output a₁y₁(t) + a₂y₂(t).

Time invariance: If input x(t) produces output y(t), input x(t+t₀) produces output y(t+t₀), where the offset t₀ can be positive or negative.