| Line 10: | Line 10: | ||
<math>x_1(t)\rightarrow y_1(t) = 4x_1(t)</math> | <math>x_1(t)\rightarrow y_1(t) = 4x_1(t)</math> | ||
| + | <math>x_2(t)\rightarrow y_2(t) = 4x_2(t)</math> | ||
| + | <math>x_3 = ax_1(t) + bx_2(t)</math> | ||
| + | <math>y_3(t) = 4t_3(t)</math> | ||
| + | |||
| + | <math>=4(ax_1(t) + bx_2(t))</math> | ||
| + | |||
| + | <math>=4ax_1(t) + 4bx_2(t)</math> | ||
| + | |||
| + | <math>=ay_1(t) + by_2(t)</math> | ||
| + | |||
| + | so it is linear | ||
== non linear system == | == non linear system == | ||
Revision as of 10:36, 11 September 2008
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) $
$ y_3(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
