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}(\frac{k\pi}{m}) \left\cos \left( k\theta \right) +b_k\sin\left(k \theta \right) \right.
Here, the term
\mathrm{sinc}(\frac{k\pi}{m})
is the Lanczos σ factor, which is responsible for eliminating the Gibbs ringing phenomenon.

 

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