(New page: A function is said to be periodic (or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with period if f(x)=f(x+n...) |
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| − | A function is said to be periodic (or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with period if | + | A function is said to be '''periodic''' (or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with period if |
f(x)=f(x+np) | f(x)=f(x+np) | ||
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p is the Fundamental Period | p is the Fundamental Period | ||
The constant function is periodic with any period for all nonzero real numbers , so there is no concept analogous to the least period for constant functions. | The constant function is periodic with any period for all nonzero real numbers , so there is no concept analogous to the least period for constant functions. | ||
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| + | An '''aperiodic''' function never repeats, although technically an aperiodic function can be considered like a periodic function with an infinite period. | ||
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| + | f(x+p)=-f(x) | ||
Revision as of 16:21, 5 September 2008
A function is said to be periodic (or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with period if
f(x)=f(x+np)
where n=1,2.........
p is the Fundamental Period
The constant function is periodic with any period for all nonzero real numbers , so there is no concept analogous to the least period for constant functions.
An aperiodic function never repeats, although technically an aperiodic function can be considered like a periodic function with an infinite period.
f(x+p)=-f(x)
