Definition

If Z(t) and W(t) in the following are equal the system is linear.


Linearity Part 1 ECE301Fall2008mboutin.jpg



Linearity Part 2 ECE301Fall2008mboutin.jpg

Examples

Linear:

An example of an linear function is $ \ y(t) = 3x(t + 8) $

because the result of the 1st method above yields $ \ 3ax(t + 8) + 3bx(t + 8) $

and the result of the 2nd method above yields $ \ 3[ax(t + 8) + bx(t + 8)] $. Because they yield the same result the system is linear.

Non-Linear:

An example of a non-linear function is $ \ y(t) = e^{x(t)} $

because the result of the 1st method above yields $ \ e^{ax(t)} + e^{bx(t)} $

and the result of the 2nd method above yields $ \ e^{ax(t) + bx(t)} $, which is not equal to the first result.

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood