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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


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

© 1996-9 Eric W. Weisstein