Rectangular function: Difference between revisions

Revision as of 05:13, 10 December 2004

Revision as of 08:56, 10 December 2004

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The '''rectangular function''' (or '''rectangle function''') is defined as

:<math>\mathbf{rect}(t) = \left \{ \begin{matrix}
0 , & \leftmbox{if } |x \right| > \frac{1}{2} \\ [3pt]
\frac{1}{2}, & \leftmbox{if } |x \right| = \frac{1}{2} \\ [3pt]
1, & \leftmbox{if } |x \right| < \frac{1}{2}
\end{matrix} \right.</math>

or in terms of the [[Heaviside step function]]

:<math>\mathbf{rect}(t) = \mathbf{H}(t + 1/2) - \mathbf{H}(t - 1/2)</math>

The [[Fourier transform]] is

:<math>\mathbf{rect}\left(\frac{\omega}{2 W}\right) = \frac{W}{\pi} \mathbfoperatorname{sinc}(W t)</math>

where <math>"sinc</math>" is the [[sinc function]].

==See also==

*[[boxcar function]]

*[[Fourier transform]]

{{math-stub}}