Lanczos resampling

Partial plot of a discrete signal (black dots) and of its Lanczos interpolation (solid blue curve), with size parameter a equal to 1 (top), 2 (middle) and 3 (bottom). Also shown are two copies of the Lanczos kernel, shifted and scaled, corresponding to samples 4 and 11 (dashed curves).

Lanczos filtering and Lanczos resampling are two applications of a certain 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.^[1]

The filter was invented by Claude Duchon, who named it after Cornelius Lanczos due to Duchon's use of Sigma approximation in constructing the filter, a technique created by Lanczos.^[2]