2.2a LTI System

LTI System

A linear time-invariant (LTI) system $H$ is one that is both:

1. Linear, such that its system response follows the principle of superposition (composed of linearity and additivity):

2. Homogeneity: $y(\alpha x)$

3. Time-invariant, such that a time shift in its input signal results in a time shift in its output signal:
   $x(t)\to \boxed{h(n)}\to y(t)⟹x(t-t_0)\to \boxed{h(n)}\to y(t-t_0),$
   where $t_0\in \mathbb{R}$.

Examples

Linearity & Time Invariance

Are the following signals linear or time invariant?

• $y(n)=7x(n+1)$
• $y(n)=x(n)x(n-1)$
• $y(n)=e^{x(n)}$