(→Periodic Function) |
|||
| (5 intermediate revisions by the same user not shown) | |||
| Line 5: | Line 5: | ||
if <math> f(x)=f(x+np) </math> for , 2, .... | if <math> f(x)=f(x+np) </math> for , 2, .... | ||
| − | For example, the sine function <math> f(x)=sin(x) </math>, illustrated below, is periodic with least period <math> 2\pi </math> (often simply called | + | For example, the sine function <math> f(x)=sin(x) </math>, illustrated below, is periodic with least period <math> 2\pi </math> (often simply called the period) |
[[image:periodic.gif]] | [[image:periodic.gif]] | ||
| + | |||
| + | == Non-Periodic Function == | ||
| + | |||
| + | A function is said to be non-periodic with no certain pattern period. So, f(x) is not equal to f(x+np) | ||
| + | |||
| + | For example, <math> f(x)=e^x </math> | ||
| + | |||
| + | [[image:exp.gif]] | ||
Latest revision as of 14:24, 5 September 2008
Periodic Function
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) $ for , 2, ....
For example, the sine function $ f(x)=sin(x) $, illustrated below, is periodic with least period $ 2\pi $ (often simply called the period)
Non-Periodic Function
A function is said to be non-periodic with no certain pattern period. So, f(x) is not equal to f(x+np)
For example, $ f(x)=e^x $
