“Sombrero function”的意思、由来-开放百科全书

词条

Sombrero function

释义

References

A sombrero function (sometimes called besinc function or jinc function) is the 2-dimensional polar coordinate analog of the sinc function, and is so-called because it is shaped like a sombrero hat. This function is frequently used in image processing.^[2] It can be defined through the Bessel function of the first kind where {{math|ρ² {{=}} x² + y²}}.

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The normalization factor {{math|2}} makes {{math|somb(0) {{=}} 1}}. Sometimes the {{math|π}} factor is omitted, giving the following alternative definition:

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The factor of 2 is also often omitted, giving yet another definition and causing the function maximum to be 0.5:^[3]

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References

1. ^¹{{cite book | url = https://books.google.com/books?id=T_KNSWU4uz4C&pg=PA204 | title = The perception of visual information | author = William R. Hendee, Peter Neil Temple Wells | page = 204 | date = 1997-06-27 | isbn = 978-0-387-94910-9 }}
2. ^¹{{cite web |url=http://mathworld.wolfram.com/JincFunction.html |title= Jinc Function |last= Weisstein |first= Eric W. |date= |website= MathWorld--A Wolfram Web Resource |publisher= |access-date= 1 Jan 2019 |quote= }}

^[1]^[2]
}}

2 : Signal processing|Elementary special functions

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