LanczosWindow
✖
LanczosWindow
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
.
- LanczosWindow automatically threads over lists.

Examples
open allclose allBasic Examples (3)Summary of the most common use cases
Scope (4)Survey of the scope of standard use cases

https://wolfram.com/xid/0fq8dxyouu8gi-rfdjbb

Translated and dilated Lanczos window:

https://wolfram.com/xid/0fq8dxyouu8gi-fzqpy6

2D Lanczos window with a circular support:

https://wolfram.com/xid/0fq8dxyouu8gi-h4a5s3

Discrete Lanczos window of length 15:

https://wolfram.com/xid/0fq8dxyouu8gi-5yhlc9

Discrete 15×10 2D Lanczos window:

https://wolfram.com/xid/0fq8dxyouu8gi-ivcfcj

Applications (4)Sample problems that can be solved with this function
Decrease the size of an image by a factor of 5 using the Lanczos method:

https://wolfram.com/xid/0fq8dxyouu8gi-1dcwws

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

https://wolfram.com/xid/0fq8dxyouu8gi-gme0eq


https://wolfram.com/xid/0fq8dxyouu8gi-fl9fwi

Use a window specification to calculate sample PowerSpectralDensity:

https://wolfram.com/xid/0fq8dxyouu8gi-la7hx0

https://wolfram.com/xid/0fq8dxyouu8gi-xvpxo9
Compare to spectral density calculated without a windowing function:

https://wolfram.com/xid/0fq8dxyouu8gi-012m6s

https://wolfram.com/xid/0fq8dxyouu8gi-phnp33

The plot shows that window smooths the spectral density:

https://wolfram.com/xid/0fq8dxyouu8gi-z97d2x

Compare to the theoretical spectral density of the process:

https://wolfram.com/xid/0fq8dxyouu8gi-2bqb4v

Use a window specification for time series estimation:

https://wolfram.com/xid/0fq8dxyouu8gi-8tceex
Specify window for spectral estimator:

https://wolfram.com/xid/0fq8dxyouu8gi-nkbyb7

Properties & Relations (2)Properties of the function, and connections to other functions
The area under the Lanczos window:

https://wolfram.com/xid/0fq8dxyouu8gi-bvk48s

Normalize to create a window with unit area:

https://wolfram.com/xid/0fq8dxyouu8gi-uvswua

Fourier transform of the Lanczos window:

https://wolfram.com/xid/0fq8dxyouu8gi-hw628m

Power spectrum of the Lanczos window:

https://wolfram.com/xid/0fq8dxyouu8gi-6mml6t

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.
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.
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
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: 09-July-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: 09-July-2025
]}