Fourier series | Numerical analysis

Sigma approximation

In mathematics, σ-approximation adjusts a Fourier summation to greatly reduce the Gibbs phenomenon, which would otherwise occur at discontinuities. A σ-approximated summation for a series of period T can be written as follows: in terms of the normalized sinc function The term 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. (Wikipedia).

Sigma approximation
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👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic sequence is given by Sn = n/2 [2a + (n - 1)d], where a is

From playlist Series

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From playlist Series

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From playlist Series

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From playlist Series

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From playlist Series

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Related pages

Gibbs phenomenon | Mathematics | Lanczos resampling | Sinc function | Fourier series