Def of linear system
Linear system is a system that possesses the important property of superposition.(Text book P.53)
linear system
$ y(t) = 4x(t) $
$ x_1(t)\rightarrow y_1(t) = 4x_1(t) $
$ x_2(t)\rightarrow y_2(t) = 4x_2(t) $
$ x_3 = ax_1(t) + bx_2(t) $
$ w(t) = 4t_3(t) $
$ =4(ax_1(t) + bx_2(t)) $
$ =4ax_1(t) + 4bx_2(t) $
$ =ay_1(t) + by_2(t) $
so it is linear
non linear system
$ y[n] = 4x[n] + 5 $
$ x_1 \rightarrow y_1[n] = 4x_1[n] +5 = 21 $
$ x_2 \rightarrow y_2[n] = 4x_2[n] + 5 = 25 $
$ w[n] = 4[x_1[n] + x_2[n]] + 5 = 41 $
$ w[n]\neq y_1[n] + y_2[n] $
so it is non linear
