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Sigma approximation
In mathematics, σ-approximation adjusts a Fourier summation to eliminate the Gibbs phenomenon which would otherwise occur at discontinuities.
A σ-approximated summation can be written as follows,
![s(\theta) = \frac{1}{2} a_0 + \sum_{k=1}^{m-1} \mathrm{sinc}\left(\frac{k\pi}{m}\right) \left[a_{k} \cos \left( k\theta \right) +b_k\sin\left(k \theta \right) \right].](a/../upload/math/2b32682258a5a271976c512dcde14824.png)
Here, the term
is the Lanczos σ factor, which is responsible for eliminating the Gibbs ringing phenomenon.
Last updated: 05-28-2005 00:41:06
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details