Rectangular Function

The rectangular function (also known as the '''rectangle function''', '''rect function''' or the normalized ''' Boxcar Function ''') is defined as : $\mathrm{rect}(t) = \sqcap(t) = \left \{ \begin{matrix} Rac{1}{2} & \mbox{if } t rac{1}{2} \$ {Link without Title}
	Rac{1}{2} & \mbox{if } t	rac{1}{2} \

=rac{ extrm{sinc}(\omega/2)}{\sqrt{2\pi}}

where "sinc" is the Sinc Function . Viewing the rectangular function as a Probability Distribution function, its Characteristic Function is therefore written

:

arphi(k)=	extrm{sinc}(k/2)\,

M(k)=rac{	extrm{sinh}(k/2)}{k/2}\,

where "sinh" is the Hyperbolic Sine function.

SEE ALSO

	CATEGORIES ABOUT RECTANGULAR FUNCTION

	elementary special functions

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