(New page: ==Continuous Time== ===Periodic signals=== A signal is periodic if there exists some T>0 such that: <math> x(t) = x(t+T) </math>) |
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+ | =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= | ||
+ | <span style="color:green"> Read the instructor's comments [[hw1periodicECE301f08profcomments|here]]. </span> | ||
+ | |||
==Continuous Time== | ==Continuous Time== | ||
− | |||
+ | ==Periodic== | ||
A signal is periodic if there exists some T>0 such that: | A signal is periodic if there exists some T>0 such that: | ||
<math> x(t) = x(t+T) </math> | <math> x(t) = x(t+T) </math> | ||
+ | |||
+ | -Consider <math> x(t) = sin(t) </math> from 0 to 8pi | ||
+ | <center>[[Image:sin_ECE301Fall2008mboutin.jpg|400px]]</center> | ||
+ | |||
+ | |||
+ | ==Non-Periodic== | ||
+ | A signal is NOT periodic if the converse is true, there DOESN'T exists some T>0 such that: | ||
+ | x(t) = x(t+T) | ||
+ | |||
+ | -Consider <math> x(t) = e^{-t/20} * sin(2t) </math> | ||
+ | <center>[[Image:Sin_decr_ECE301Fall2008mboutin.jpg|400px]]</center> |
Latest revision as of 07:08, 14 April 2010
Contents
Periodic versus non-periodic functions (hw1, ECE301)
Read the instructor's comments here.
Continuous Time
Periodic
A signal is periodic if there exists some T>0 such that: $ x(t) = x(t+T) $
-Consider $ x(t) = sin(t) $ from 0 to 8pi
![Sin ECE301Fall2008mboutin.jpg](/rhea/images/thumb/e/eb/Sin_ECE301Fall2008mboutin.jpg/400px-Sin_ECE301Fall2008mboutin.jpg)
Non-Periodic
A signal is NOT periodic if the converse is true, there DOESN'T exists some T>0 such that: x(t) = x(t+T)
-Consider $ x(t) = e^{-t/20} * sin(2t) $
![Sin decr ECE301Fall2008mboutin.jpg](/rhea/images/thumb/4/4a/Sin_decr_ECE301Fall2008mboutin.jpg/400px-Sin_decr_ECE301Fall2008mboutin.jpg)