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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: | 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: | ||
| − | <math>rep_T</math> = <math>x(t)* P_T (t) </math> | + | <math>rep_T </math> = <math>x(t)* P_T (t) </math> |
| − | + | = <math>x(t)* \sum_{k=-\infty}^{\infty}\delta(t-kT) </math> | |
| − | + | = <math>\sum_{k=-\infty}^{\infty}x(t) * \delta(t-kT) </math> | |
| − | + | = <math>\sum_{k=-\infty}^{\infty}x(t-kT) </math> | |
| − | + | If below is the x(t): | |
| + | [[Image:function.jpg]] | ||
| + | |||
| + | Then the <math>rep_T x(t)</math> looks like: | ||
| + | [[Image:repped.jpg]] | ||
Revision as of 07:52, 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:
