(→Non-Periodic Function) |
(→Periodic Function) |
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Periodic function of CT is <math>y(t)=sin(t)</math>. | Periodic function of CT is <math>y(t)=sin(t)</math>. | ||
+ | <pre> | ||
Proof: <math>y(t+T)= sin(t+T)</math>,where we take <math>T=2*pi</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)=sin(t)</math> | so <math>sin(t+T)=sin(t+2*pi)=sin(t)</math> | ||
i.e <math>y(t+T)=y(t)</math>. | i.e <math>y(t+T)=y(t)</math>. | ||
so it's periodic function. | so it's periodic function. | ||
+ | </pre> | ||
== Non-Periodic Function == | == Non-Periodic Function == |
Revision as of 17:39, 2 September 2008
Periodic Function
Periodic function of CT is $ y(t)=sin(t) $.
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)=sin(t)</math> i.e <math>y(t+T)=y(t)</math>. 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