(→Periodic signals) |
(→Periodic signals) |
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==Continuous Time== | ==Continuous Time== | ||
| − | === | + | ===Continuous Time=== |
| − | + | ==Periodic== | |
A signal is periodic if there exists some T>0 such that: | A signal is periodic if there exists some T>0 such that: | ||
<math> x(t) = x(t+T) </math> | <math> x(t) = x(t+T) </math> | ||
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<center>[[Image:sin.jpg _ECE301Fall2008mboutin|400px]]</center> | <center>[[Image:sin.jpg _ECE301Fall2008mboutin|400px]]</center> | ||
| + | |||
| + | ==Non-Periodic== | ||
A signal is NOT periodic if the converse is true, there exists some T>0 such that: | A signal is NOT periodic if the converse is true, there exists some T>0 such that: | ||
x(t) ≠ x(t+T) | x(t) ≠ x(t+T) | ||
| − | -Consider <math> x(t) = e^{-t/20} * sin(2t) </math> | + | -Consider <math> x(t) = e^{-t/20} * sin(2t) </math> |
<center>[[Image:Sin_decr.jpg _ECE301Fall2008mboutin|400px]]</center> | <center>[[Image:Sin_decr.jpg _ECE301Fall2008mboutin|400px]]</center> | ||
Revision as of 08:53, 5 September 2008
Continuous Time
Continuous Time
Periodic
A signal is periodic if there exists some T>0 such that: $ x(t) = x(t+T) $
-Consider $ x(t) = sin(t) $ from 0 to 8pi
Non-Periodic
A signal is NOT periodic if the converse is true, there exists some T>0 such that: x(t) ≠ x(t+T)
-Consider $ x(t) = e^{-t/20} * sin(2t) $
