Lanczos resampling

Lanczos resampling and Lanczos filtering are two applications of a mathematical formula. It can be used as a low-pass filter or used to smoothly interpolate the value of a digital signal between its samples. In the latter case it maps each sample of the given signal to a translated and scaled copy of the Lanczos kernel, which is a sinc function windowed by the central lobe of a second, longer, sinc function. The sum of these translated and scaled kernels is then evaluated at the desired points.

Lanczos resampling is typically used to increase the sampling rate of a digital signal, or to shift it by a fraction of the sampling interval. It is often used also for multivariate interpolation, for example to resize or rotate a digital image. It has been considered the "best compromise" among several simple filters for this purpose.

The filter is named after its inventor, Cornelius Lanczos (Hungarian pronunciation: [ˈlaːnt͡soʃ]).

The effect of each input sample on the interpolated values is defined by the filter's reconstruction kernel L(x), called the Lanczos kernel. It is the normalized sinc function sinc(x), windowed (multiplied) by the Lanczos window, or sinc window, which is the central lobe of a horizontally-stretched sinc function sinc(x/a) for  −a ≤ x ≤ a.

Equivalently,

The parameter a is a positive integer, typically 2 or 3, which determines the size of the kernel. The Lanczos kernel has 2a − 1 lobes, a positive one at the center and a − 1 alternating negative and positive lobes on each side.

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