ExactBlackmanWindow
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ExactBlackmanWindow
Details

- ExactBlackmanWindow is a window function typically used for finite impulse response (FIR) filter design and spectral analysis.
- 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.
- ExactBlackmanWindow[x] is equal to
- ExactBlackmanWindow automatically threads over lists.

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

https://wolfram.com/xid/0elum80g16n8hhu-55nvy5

Shape of a 2D exact Blackman window:

https://wolfram.com/xid/0elum80g16n8hhu-yyuiog

Extract the continuous function representing the exact Blackman window:

https://wolfram.com/xid/0elum80g16n8hhu-i5bqnh

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

https://wolfram.com/xid/0elum80g16n8hhu-rfdjbb

Translated and dilated exact Blackman window:

https://wolfram.com/xid/0elum80g16n8hhu-fzqpy6

2D exact Blackman window with a circular support:

https://wolfram.com/xid/0elum80g16n8hhu-h4a5s3

Discrete exact Blackman window of length 15:

https://wolfram.com/xid/0elum80g16n8hhu-5yhlc9

Discrete 15×10 2D exact Blackman window:

https://wolfram.com/xid/0elum80g16n8hhu-ivcfcj

Applications (3)Sample problems that can be solved with this function
Create a moving average filter of length 11:

https://wolfram.com/xid/0elum80g16n8hhu-b4svbb

Smooth the filter using a exact Blackman window:

https://wolfram.com/xid/0elum80g16n8hhu-1k06dy
Log-magnitude plot of the frequency spectrum of the filters:

https://wolfram.com/xid/0elum80g16n8hhu-65dzhv

Use a window specification to calculate sample PowerSpectralDensity:

https://wolfram.com/xid/0elum80g16n8hhu-la7hx0

https://wolfram.com/xid/0elum80g16n8hhu-xvpxo9
Compare to spectral density calculated without a windowing function:

https://wolfram.com/xid/0elum80g16n8hhu-012m6s

https://wolfram.com/xid/0elum80g16n8hhu-phnp33

The plot shows that window smooths the spectral density:

https://wolfram.com/xid/0elum80g16n8hhu-z97d2x

Compare to the theoretical spectral density of the process:

https://wolfram.com/xid/0elum80g16n8hhu-2bqb4v

Use a window specification for time series estimation:

https://wolfram.com/xid/0elum80g16n8hhu-8tceex
Specify window for spectral estimator:

https://wolfram.com/xid/0elum80g16n8hhu-nkbyb7

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

https://wolfram.com/xid/0elum80g16n8hhu-bvk48s

Normalize to create a window with unit area:

https://wolfram.com/xid/0elum80g16n8hhu-uvswua

Fourier transform of the exact Blackman window:

https://wolfram.com/xid/0elum80g16n8hhu-hw628m

Power spectrum of the exact Blackman window:

https://wolfram.com/xid/0elum80g16n8hhu-6mml6t

Wolfram Research (2012), ExactBlackmanWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html.
Text
Wolfram Research (2012), ExactBlackmanWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html.
Wolfram Research (2012), ExactBlackmanWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html.
CMS
Wolfram Language. 2012. "ExactBlackmanWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html.
Wolfram Language. 2012. "ExactBlackmanWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html.
APA
Wolfram Language. (2012). ExactBlackmanWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html
Wolfram Language. (2012). ExactBlackmanWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html
BibTeX
@misc{reference.wolfram_2025_exactblackmanwindow, author="Wolfram Research", title="{ExactBlackmanWindow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html}", note=[Accessed: 10-July-2025
]}
BibLaTeX
@online{reference.wolfram_2025_exactblackmanwindow, organization={Wolfram Research}, title={ExactBlackmanWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/ExactBlackmanWindow.html}, note=[Accessed: 10-July-2025
]}