(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...) |
(→Non-Periodic Function) |
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Proof: assume y(t) is periodic, then there exists a non-zero T,that makes<math>y(t+T)=y(t)</math> | Proof: assume y(t) is periodic, then there exists a non-zero T,that makes<math>y(t+T)=y(t)</math> | ||
i.e. <math>t+T=t</math>,so <math>T=0</math>,which violates the assumption. | i.e. <math>t+T=t</math>,so <math>T=0</math>,which violates the assumption. | ||
| − | So y(t)=t is a non-periodic function | + | So <math>y(t)=t</math> is a non-periodic function |
Revision as of 17:38, 2 September 2008
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
