Lanczos Sigma Factor

Writing a Fourier Series as

$$f(\theta)={\textstyle{1\over 2}}a_0+\sum_{n=1}^m \mathop{\rm... ...left({n\pi\over 2m}\right)[a_n\cos(n\theta)+b_n\sin(n\theta)],$$

where $m$ is the last term and the $\mathop{\rm sinc}\nolimits x$ terms are the Lanczos $\sigma$ factor, removes the Gibbs Phenomenon (Acton 1990).

See also Fourier Series, Gibbs Phenomenon, Sinc Function

References

Acton, F. S. Numerical Methods That Work, 2nd printing. Washington, DC: Math. Assoc. Amer., p. 228, 1990.