Rectangular function

The rectangular function is defined as, Alternate definitions of the function define to be 0, 1, or undefined. We can also express the rectangular function in terms of the Heaviside step function Heaviside step function

The Heaviside step function, sometimes called the unit step function [i] and named in honor of Oliver Heaviside [i] ...

, : or, alternatively: The rectangular function is normalized: The unitary Fourier transforms of the rectangular function are, , and, in terms of the normalized sinc function Sinc function

The sinc function, denoted by , has two definitions, sometimes distinguished as the normalized sinc ...

, We can define the triangular function Triangular function

The triangular function is defined as: ...

as the convolution of two rectangular functions: Viewing the rectangular function as a probability distribution Probability distribution

In mathematics [i] and statistics [i], a probability distribution, more properly called a probability ...

function, its characteristic function is,

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The rectangular function is defined as,

Alternate definitions of the function define to be 0, 1, or undefined. We can also express the rectangular function in terms of the Heaviside step function Heaviside step function

The Heaviside step function, sometimes called the unit step function [i] and named in honor of Oliver Heaviside [i] ...

, :

or, alternatively:

The rectangular function is normalized:

The unitary Fourier transforms of the rectangular function are,

,

and, in terms of the normalized sinc function Sinc function

The sinc function, denoted by , has two definitions, sometimes distinguished as the normalized sinc ...

,

We can define the triangular function Triangular function

The triangular function is defined as:
...

as the convolution of two rectangular functions:

Viewing the rectangular function as a probability distribution Probability distribution

In mathematics [i] and statistics [i], a probability distribution, more properly called a probability...

function, its characteristic function is,

and its moment generating function is,

where is the hyperbolic sine Hyperbolic function

In mathematics [i], the hyperbolic functions are analogs of the ordinary trigonometric [i]...

function.

Rectangular function

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