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'''Rep Function:''' | '''Rep Function:''' | ||
| − | A rep function periodically repeats another function with some specified period T. Mathematically a rep operator is | + | 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> | |
Revision as of 05:58, 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) $
