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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 Function == | == Periodic Function == | ||
| − | Periodic function of CT is | + | Periodic function of CT is y(t)=sin(t). |
<pre> | <pre> | ||
| − | Proof: | + | Proof: y(t+T)= sin(t+T),where we take T=2*pi. |
| − | so | + | so sin(t+T)=sin(t+2*pi)=sin(t) |
| − | i.e | + | i.e y(t+T)=y(t). |
so it's periodic function. | so it's periodic function. | ||
</pre> | </pre> | ||
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Non-periodic function is <math>y(t)=t</math>. | Non-periodic function is <math>y(t)=t</math>. | ||
| − | Proof: assume y(t) is periodic, then there exists a non-zero T,that makes | + | <pre> |
| − | i.e. | + | Proof: assume y(t) is periodic, then there exists a non-zero T,that makes y(t+T)=y(t) |
| − | So | + | i.e. t+T=t,so T=0,which violates the assumption. |
| + | So y(t)=t is a non-periodic function | ||
| + | </pre> | ||
Latest revision as of 07:17, 14 April 2010
Periodic versus non-periodic functions (hw1, ECE301)
Read the instructor's comments here.
Periodic Function
Periodic function of CT is y(t)=sin(t).
Proof: y(t+T)= sin(t+T),where we take T=2*pi.
so sin(t+T)=sin(t+2*pi)=sin(t)
i.e y(t+T)=y(t).
so it's periodic function.
Non-Periodic Function
Non-periodic function is $ y(t)=t $.
Proof: assume y(t) is periodic, then there exists a non-zero T,that makes y(t+T)=y(t)
i.e. t+T=t,so T=0,which violates the assumption.
So y(t)=t is a non-periodic function
