LanczosWindow

LanczosWindow[x]

represents a Lanczos window function of x.

Details

  • LanczosWindow, also known as the sinc window, is typically used for antialiasing and resampling.
  • Window functions are used in applications where data is processed in short segments and have a smoothing effect by gradually tapering data values to zero at the ends of each segment.
  • LanczosWindow[x] is equal to  (sin(2 pi x))/(2 pi x) -1/2<=x<=1/2; 0 TemplateBox[{x}, Abs]>1/2; .
  • LanczosWindow automatically threads over lists.

Examples

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Basic Examples  (3)

Shape of a 1D Lanczos window:

Shape of a 2D Lanczos window:

Extract the continuous function representing the Lanczos window:

Scope  (4)

Evaluate numerically:

Translated and dilated Lanczos window:

2D Lanczos window with a circular support:

Discrete Lanczos window of length 15:

Discrete 15×10 2D Lanczos window:

Applications  (4)

Decrease the size of an image by a factor of 5 using the Lanczos method:

By default, "Lanczos" resampling is used when resampling audio signals:

Use a window specification to calculate sample PowerSpectralDensity:

Calculate the spectrum:

Compare to spectral density calculated without a windowing function:

The plot shows that window smooths the spectral density:

Compare to the theoretical spectral density of the process:

Use a window specification for time series estimation:

Specify window for spectral estimator:

Properties & Relations  (2)

The area under the Lanczos window:

Normalize to create a window with unit area:

Fourier transform of the Lanczos window:

Power spectrum of the Lanczos window:

Wolfram Research (2012), LanczosWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/LanczosWindow.html.

Text

Wolfram Research (2012), LanczosWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/LanczosWindow.html.

CMS

Wolfram Language. 2012. "LanczosWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LanczosWindow.html.

APA

Wolfram Language. (2012). LanczosWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LanczosWindow.html

BibTeX

@misc{reference.wolfram_2025_lanczoswindow, author="Wolfram Research", title="{LanczosWindow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/LanczosWindow.html}", note=[Accessed: 22-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_lanczoswindow, organization={Wolfram Research}, title={LanczosWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/LanczosWindow.html}, note=[Accessed: 22-February-2025 ]}