The Basics of Linearity
A system is linear if its inputs are sequentially equal to the outputs for a certain function:
$ x(t) = a*x1(t) + b*x2(t) = a*y1(t) + b*y2(t) $
Take for a simple example:
Ex) What is the output of:
$ x[n] = e^{j*pi*n} -> n*e^{-j*pi*n} $
$ x[n] \to Sys 1 \to n*x[-n] $
from:
$ e^{j*n*y} = cos(n*y) + j*sin(n*y) \pi $
we determine: x[n] = cos(
