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<math>x(t) = sin(t)</math> | <math>x(t) = sin(t)</math> | ||
| − | Clearly, <math>x(t)</math> is periodic because there is a <math>T > 0</math> such that <math>x(t + T) = x(t)</math> for all <math>t</math>. An obvious example for <math>t</math> would be <math>t = 2\pi</math>. | + | Clearly, <math>x(t)</math> is periodic because there is a <math>T > 0</math> such that <math>x(t + T) = x(t)</math> for all <math>t</math>. An obvious example for <math>t</math> would be <math>t = 2\pi</math>. Shifting <math>x(t)</math> by <math>2\pi</math> gives the original function since <math>2\pi</math> is the ''fundamental period'' of <math>x(t) = sin(t)</math> |
Revision as of 21:15, 4 September 2008
A Periodic Function
$ x(t) = sin(t) $
Clearly, $ x(t) $ is periodic because there is a $ T > 0 $ such that $ x(t + T) = x(t) $ for all $ t $. An obvious example for $ t $ would be $ t = 2\pi $. Shifting $ x(t) $ by $ 2\pi $ gives the original function since $ 2\pi $ is the fundamental period of $ x(t) = sin(t) $
