Sigma approximation: Difference between revisions

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Revision as of 01:15, 7 February 2017

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In [[mathematics]], '''σ-approximation''' adjusts a [[Fourier series|Fourier summation]] to eliminategreatly reduce the [[Gibbs phenomenon]] which would otherwise occur at [[Discontinuity (mathematics)|discontinuities]].

A σ-approximated summation for a series of period ''T'' can be written as follows:

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:<math>\mathrm{sinc}\Bigl(\frac{k}{m}\Bigr)</math>

is the '''Lanczos σ factor''', which is responsible for eliminating most of the Gibbs phenomenon. It does not do so entirely, however, but one can square or even cube the expression to serially attenuate Gibbs Phenomenon in the most extreme cases.

== See also ==