FlatTopWindow
✖
FlatTopWindow
Details

- FlatTopWindow is a window function typically used in signal processing applications where data needs to be processed in short segments.
- Window functions have a smoothing effect by gradually tapering data values to zero at the ends of each segment.
- FlatTopWindow[x] is equal to
.
- FlatTopWindow automatically threads over lists.

Examples
open allclose allBasic Examples (3)Summary of the most common use cases
Shape of a 1D exact flat top window:

https://wolfram.com/xid/0btnh636hn5u-55nvy5

Shape of a 2D exact flat top window:

https://wolfram.com/xid/0btnh636hn5u-yyuiog

Extract the continuous function representing the exact flat top window:

https://wolfram.com/xid/0btnh636hn5u-i5bqnh

Scope (4)Survey of the scope of standard use cases

https://wolfram.com/xid/0btnh636hn5u-rfdjbb

Translated and dilated exact flat top window:

https://wolfram.com/xid/0btnh636hn5u-fzqpy6

2D exact flat top window with a circular support:

https://wolfram.com/xid/0btnh636hn5u-h4a5s3

Discrete exact flat top window of length 15:

https://wolfram.com/xid/0btnh636hn5u-5yhlc9

Discrete 15×10 2D flat top window:

https://wolfram.com/xid/0btnh636hn5u-ivcfcj

Applications (3)Sample problems that can be solved with this function
Create a moving average filter of length 21:

https://wolfram.com/xid/0btnh636hn5u-b4svbb

Taper the filter using a flat top window:

https://wolfram.com/xid/0btnh636hn5u-1k06dy
Log-magnitude plot of the power spectra of the filters:

https://wolfram.com/xid/0btnh636hn5u-65dzhv

Use a window specification to calculate sample PowerSpectralDensity:

https://wolfram.com/xid/0btnh636hn5u-la7hx0

https://wolfram.com/xid/0btnh636hn5u-xvpxo9
Compare to spectral density calculated without a windowing function:

https://wolfram.com/xid/0btnh636hn5u-012m6s

https://wolfram.com/xid/0btnh636hn5u-phnp33

The plot shows that window smooths the spectral density:

https://wolfram.com/xid/0btnh636hn5u-z97d2x

Compare to the theoretical spectral density of the process:

https://wolfram.com/xid/0btnh636hn5u-2bqb4v

Use a window specification for time series estimation:

https://wolfram.com/xid/0btnh636hn5u-8tceex
Specify window for spectral estimator:

https://wolfram.com/xid/0btnh636hn5u-nkbyb7

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

https://wolfram.com/xid/0btnh636hn5u-bvk48s

Normalize to create a window with unit area:

https://wolfram.com/xid/0btnh636hn5u-uvswua

Fourier transform of the exact flat top window:

https://wolfram.com/xid/0btnh636hn5u-hw628m

Power spectrum of the exact flat top window:

https://wolfram.com/xid/0btnh636hn5u-6mml6t

Wolfram Research (2012), FlatTopWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/FlatTopWindow.html.
Text
Wolfram Research (2012), FlatTopWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/FlatTopWindow.html.
Wolfram Research (2012), FlatTopWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/FlatTopWindow.html.
CMS
Wolfram Language. 2012. "FlatTopWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FlatTopWindow.html.
Wolfram Language. 2012. "FlatTopWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FlatTopWindow.html.
APA
Wolfram Language. (2012). FlatTopWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FlatTopWindow.html
Wolfram Language. (2012). FlatTopWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FlatTopWindow.html
BibTeX
@misc{reference.wolfram_2025_flattopwindow, author="Wolfram Research", title="{FlatTopWindow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/FlatTopWindow.html}", note=[Accessed: 10-July-2025
]}
BibLaTeX
@online{reference.wolfram_2025_flattopwindow, organization={Wolfram Research}, title={FlatTopWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/FlatTopWindow.html}, note=[Accessed: 10-July-2025
]}