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If below is the x(t): | If below is the x(t): | ||
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Then the <math>rep_T x(t)</math> looks like: | Then the <math>rep_T x(t)</math> looks like: | ||
[[Image:repped.jpg]] | [[Image:repped.jpg]] | ||
Revision as of 07:56, 23 September 2009
Rep Function:
A rep function periodically repeats another function with some specified period T ( basically sampling time). Mathematically a rep operator is a function x(t) convoluted with a summation of shifted deltas:
$ rep_T $ = $ x(t)* P_T (t) $
= $ x(t)* \sum_{k=-\infty}^{\infty}\delta(t-kT) $
= $ \sum_{k=-\infty}^{\infty}x(t) * \delta(t-kT) $
= $ \sum_{k=-\infty}^{\infty}x(t-kT) $
If below is the x(t):
Then the $ rep_T x(t) $ looks like:
