| Line 3: | Line 3: | ||
<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 | + | 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 choice 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 21:16, 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 choice 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) $
