CosineWindow[x]
represents a cosine window function of x.
CosineWindow[x,α]
uses the exponent α.


CosineWindow
CosineWindow[x]
represents a cosine window function of x.
CosineWindow[x,α]
uses the exponent α.
Details

- CosineWindow 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.
- CosineWindow[x,α] is equal to
for
and 0 otherwise.
- CosineWindow[x] is equivalent to CosineWindow[x,1].
- CosineWindow automatically threads over lists.

Examples
open all close allBasic Examples (3)
Scope (6)
Applications (3)
Create a moving-average filter of length 11:
Taper the filter using a cosine window:
Log-magnitude plot of the power spectra of the two filters:
Use a window specification to calculate sample PowerSpectralDensity:
Compare to spectral density calculated without a windowing function:
The plot shows that the window smooths the spectral density:
Compare to the theoretical spectral density of the process:
Properties & Relations (3)
CosineWindow[x,0] is equivalent to a Dirichlet window:
The area under the cosine window:
Normalize to create a window with unit area:
Possible Issues (1)
2D sampling of cosine window uses a different exponent for each row of samples when passed as a symbol to Array:
Related Guides
History
Text
Wolfram Research (2012), CosineWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/CosineWindow.html.
CMS
Wolfram Language. 2012. "CosineWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CosineWindow.html.
APA
Wolfram Language. (2012). CosineWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CosineWindow.html
BibTeX
@misc{reference.wolfram_2025_cosinewindow, author="Wolfram Research", title="{CosineWindow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/CosineWindow.html}", note=[Accessed: 09-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_cosinewindow, organization={Wolfram Research}, title={CosineWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/CosineWindow.html}, note=[Accessed: 09-August-2025]}