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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> | ||
+ | |||
== Periodic Functions in Continuous Time == | == Periodic Functions in Continuous Time == | ||
− | * Functions are classified as periodic if there exists <math>T\!</math> such that <math>y(x+T)=y(x)\!</math>. | + | * Functions are classified as periodic if there exists <math>T>0\!</math> such that <math>y(x+T)=y(x)\!</math>. |
<br> | <br> | ||
The following is an example of a periodic function: | The following is an example of a periodic function: | ||
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<center>[[Image:Sinpix_ECE301Fall2008mboutin.jpg]]</center> | <center>[[Image:Sinpix_ECE301Fall2008mboutin.jpg]]</center> | ||
− | This function is periodic because <math>y(x)=y(x+T)\!</math> for <math>T= | + | This function is periodic because <math>y(x)=y(x+T)\!</math> for <math>T=2, 4, 6\!</math> etc. |
− | + | ||
== Non-Periodic Functions in Continuous Time == | == Non-Periodic Functions in Continuous Time == | ||
− | * Functions are classified as non-periodic if there exists no <math>T\!</math> such that <math>y(x+T)=y(x)\!</math>. | + | * Functions are classified as non-periodic if there exists no <math>T>0\!</math> such that <math>y(x+T)=y(x)\!</math>. |
<br> | <br> | ||
The following is an example of a non-periodic function: | The following is an example of a non-periodic function: |
Latest revision as of 07:19, 14 April 2010
Periodic versus non-periodic functions (hw1, ECE301)
Read the instructor's comments here.
Periodic Functions in Continuous Time
- Functions are classified as periodic if there exists $ T>0\! $ such that $ y(x+T)=y(x)\! $.
The following is an example of a periodic function:
This function is periodic because $ y(x)=y(x+T)\! $ for $ T=2, 4, 6\! $ etc.
Non-Periodic Functions in Continuous Time
- Functions are classified as non-periodic if there exists no $ T>0\! $ such that $ y(x+T)=y(x)\! $.
The following is an example of a non-periodic function:
This function is not periodic because there exists no T where $ y(x)=y(x+T)\! $.