L ( x ) = of all integer-translated copies of the kernel is not always 1. 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. The effect of each input sample on the interpolated values is defined by the filter's reconstruction kernel L( x), called the Lanczos kernel. Note that the function obtains negative values. Lanczos kernels for the cases a = 2 and a = 3. The filter is named after its inventor, Cornelius Lanczos ( Hungarian pronunciation: ). It has been considered the "best compromise" among several simple filters for this purpose.
It is often used also for multivariate interpolation, for example to resize or rotate a digital image. 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. The sum of these translated and scaled kernels is then evaluated at the desired points. 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. It can be used as a low-pass filter or used to smoothly interpolate the value of a digital signal between its samples. Lanczos filtering and Lanczos resampling are two applications of a mathematical formula. Also shown are two copies of the Lanczos kernel, shifted and scaled, corresponding to samples 4 and 11 (dashed curves). 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).
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