Loading web-font TeX/Math/Italic
(Example of a Time Invariant System)
(Example of a Time Invariant System)
Line 15: Line 15:
 
Let <math>y(t)=2x(t)+2\!</math>.  The system is time invarient if for input <math>x(t-t_0)\!</math> the response is <math>y(t-t_0)=2x(t-t_0)+2\!</math>.
 
Let <math>y(t)=2x(t)+2\!</math>.  The system is time invarient if for input <math>x(t-t_0)\!</math> the response is <math>y(t-t_0)=2x(t-t_0)+2\!</math>.
 
<br>
 
<br>
 
Proof:
 
 
<br>
 
<br>
 +
Proof:
 +
 
<br>
 
<br>
 
[[Image:Timinvar_ECE301Fall2008mboutin.JPG]]
 
[[Image:Timinvar_ECE301Fall2008mboutin.JPG]]
  
 
== Example of a System that is not Time Invariant ==
 
== Example of a System that is not Time Invariant ==

Revision as of 12:37, 11 September 2008

Time Invariance

A system is time-invariant if for any input $ x(t)\! $ and any $ t_0\! $ (where $ t_0\! $ is a real number) the response to the shifted input $ x(t-t_0)\! $ is $ y(t-t_0)\! $.

One can show a system is time invarient by proving

Timeproof ECE301Fall2008mboutin.JPG

where $ y_1(t)\! $ and $ y_2(t)\! $ are equal.

Example of a Time Invariant System

Let $ y(t)=2x(t)+2\! $. The system is time invarient if for input $ x(t-t_0)\! $ the response is $ y(t-t_0)=2x(t-t_0)+2\! $.

Proof:


Timinvar ECE301Fall2008mboutin.JPG

Example of a System that is not Time Invariant

Alumni Liaison

Questions/answers with a recent ECE grad

Ryne Rayburn