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<math>\,\!cos(t)=cos(t+2\pi)</math> | <math>\,\!cos(t)=cos(t+2\pi)</math> | ||
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| + | <math>\,\!sin(t)=sin(t+4\pi)</math> | ||
This example can be shown to be periodic by drawing a graph, or simply computing values | This example can be shown to be periodic by drawing a graph, or simply computing values | ||
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<math>\,\!cos(\pi+2\pi)=cos(\pi)=-1</math> | <math>\,\!cos(\pi+2\pi)=cos(\pi)=-1</math> | ||
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also, any square, triangle, or sawtooth waves are periodic | also, any square, triangle, or sawtooth waves are periodic | ||
Revision as of 12:33, 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) $
This example can be shown to be periodic by drawing a graph, or simply computing values
$ \,\!t=\pi $
$ \,\!cos(\pi+2\pi)=cos(\pi)=-1 $
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.
