(→Periodic Function) |
(→Non-Periodic Function) |
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Non-periodic function is <math>y(t)=t</math>. | Non-periodic function is <math>y(t)=t</math>. | ||
| + | <pre> | ||
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 <math>y(t)=t</math> is a non-periodic function | So <math>y(t)=t</math> is a non-periodic function | ||
| + | </pre> | ||
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<math>y(t+T)=y(t)</math>
i.e. <math>t+T=t</math>,so <math>T=0</math>,which violates the assumption.
So <math>y(t)=t</math> is a non-periodic function
