System

Linear System

A system is defined as a linear system if it has the two properties:

1. Homogeneity: $h(ax)=a\cdot h(x)$
2. Superposition: $h(x_1)+h(x_2)=h(x_1+x_2)$

Serendipity with Linear Transformation.

combining both: $a{y}_1(t)+b{y}_2(t)=h(a{x}_1(t)+b{x}_2(t))$

Definition 5: Linearity

A system S is linear if it has the property that if f(t) and g(t) are input signals and $\alpha ,\beta \in C$ then $S(\alpha f_1+\beta f_2)=\alpha S(f_1)+\beta S(f_2)$