Revision as of 14:36, 11 September 2008 by Cztan (Talk)

Linearity

In my own words, a linear system is a system in which superposition applies. For example, if two inputs x1(t) and x2(t) are applied to the system, the output of the system will the sum of the responses to both inputs, y(t) = y1(t) + y2(t).

For example,

x1(t) + x2(t) $ \rightarrow $ system $ \rightarrow $ y(t) = y1(t) + y2(t)


System ECE301Fall2008mboutin.JPG

Linear System

x[n] $ \rightarrow $ system $ \rightarrow $ y[n] = 2x[n]

Proof:

System1 ECE301Fall2008mboutin.jpg

System2 ECE301Fall2008mboutin.jpg


Based on Prof Mimi's definition 3 of Linearity, since the system produces the same output for both cases, the system is linear.

Non-Linear System

x[n] $ \rightarrow $ system $ \rightarrow $ $ y[n] = x[n]^2 $

Proof:

System3 ECE301Fall2008mboutin.jpg

Alumni Liaison

Questions/answers with a recent ECE grad

Ryne Rayburn