(New page: == Periodic Function == Periodic function of CT is <math>y(t)=sin(t)</math>. Proof: <math>y(t+T)= sin(t+T)</math>,where we take <math>T=2*pi</math>. so <math>sin(t+T)=sin(t+2*pi)=s...) |
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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). |
− | Proof: | + | <pre> |
− | so | + | Proof: y(t+T)= sin(t+T),where we take T=2*pi. |
− | i.e | + | so sin(t+T)=sin(t+2*pi)=sin(t) |
+ | i.e y(t+T)=y(t). | ||
so it's periodic function. | so it's periodic function. | ||
+ | </pre> | ||
== Non-Periodic Function == | == Non-Periodic Function == | ||
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) |
+ | i.e. t+T=t,so T=0,which violates the assumption. | ||
So y(t)=t is a non-periodic function | 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