(New page: '''Rep Function:''' A rep function periodically repeats another function with some specified period T. Mathematically a rep operator is the function x(t) convoluted with a summation of sh...) |
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A rep function periodically repeats another function with some specified period T. Mathematically a rep operator is the function x(t) convoluted with a summation of shifted deltas: | A rep function periodically repeats another function with some specified period T. Mathematically a rep operator is the function x(t) convoluted with a summation of shifted deltas: | ||
| − | <math>rep_T</math> = x(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> | ||
Revision as of 05:54, 23 September 2009
Rep Function:
A rep function periodically repeats another function with some specified period T. Mathematically a rep operator is the 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) $
