Rectangular Function

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

=rac{1}{\sqrt{2\pi}}\cdot \mathrm{sinc}\left(rac{\omega}{2\pi} ight),

and, in terms of the normalized Sinc Function ,

:

\int_{-\infty}^\infty \mathrm{rect}(t)\cdot e^{-i 2\pi f t} \, dt
= \mathrm{sinc}(f)

We can define the Triangular Function as the convolution of two rectangular functions:

Viewing the rectangular function as a Probability Distribution function, its Characteristic Function is,

:

arphi(k) = rac{\sin(k/2)}{k/2}\,

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

where

\mathrm{sinh}(t)

is the Hyperbolic Sine function.

SEE ALSO

	CATEGORIES ABOUT RECTANGULAR FUNCTION

	elementary special functions

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