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== Periodic and Non-Periodic functions == | == Periodic and Non-Periodic functions == | ||
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== Examples of periodic and non-periodic functions == | == Examples of periodic and non-periodic functions == | ||
| − | Periodic examples:Basically any trigonometric function | + | |
| + | === Periodic examples:Basically any trigonometric function === | ||
<math>\,\!cos(t)=cos(t+2\pi)</math> | <math>\,\!cos(t)=cos(t+2\pi)</math> | ||
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also, any square, triangle, or sawtooth waves are periodic | also, any square, triangle, or sawtooth waves are periodic | ||
| − | + | === Non-Periodic examples === | |
| − | Non-Periodic examples | + | |
any algebraic function: | any algebraic function: | ||
Revision as of 13:29, 4 September 2008
Contents
Periodic and Non-Periodic functions
Definition
A function is defined as periodic if it can be moved along the x axis to a place where it exactly matches its original form. In mathematical terms, x(t) is periodic if and only if:
$ \,\! x(t+T)=x(t) $
Examples of periodic and non-periodic functions
Periodic examples:Basically any trigonometric function
$ \,\!cos(t)=cos(t+2\pi) $
$ \,\!sin(t)=sin(t+4\pi) $
also, any square, triangle, or sawtooth waves are periodic
Non-Periodic examples
any algebraic function:
$ \,\!f(t)=2x+5 $
$ f(t)=\frac{2x^3+5}{4^x-x} $
$ \,\!f(t)=log(x)+e^{x+2} $
any power, exponential or logarithmic function, without a periodic portion, are non-periodic as well.
