represents a Poisson window function of x.
PoissonWindow[x,α]
uses the parameter α.


PoissonWindow
represents a Poisson window function of x.
PoissonWindow[x,α]
uses the parameter α.
Details

- PoissonWindow, also known as the exponential window, 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.
- PoissonWindow[x,α] is equal to
.
- PoissonWindow[x] is equivalent to PoissonWindow[x,3].
- PoissonWindow automatically threads over lists.

Examples
open all close allBasic Examples (3)
Scope (6)
Applications (3)
Use the Poisson window to diminish the effect of signal partitioning when computing the spectrogram:
Use a window specification to calculate sample PowerSpectralDensity:
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:
Properties & Relations (3)
The area under the Poisson window:
Normalize to create a window with unit area:
Fourier transform of the Poisson window:
Power spectrum of the Poisson window:
Fourier transform of the parametrized Poisson window:
Variation of the magnitude spectrum of the Kaiser window as a function of the parameter :
Possible Issues (1)
2D sampling of Poisson window will use a different parameter for each row of samples when passed as a symbol to Array:
Related Guides
History
Text
Wolfram Research (2012), PoissonWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/PoissonWindow.html.
CMS
Wolfram Language. 2012. "PoissonWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PoissonWindow.html.
APA
Wolfram Language. (2012). PoissonWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PoissonWindow.html
BibTeX
@misc{reference.wolfram_2025_poissonwindow, author="Wolfram Research", title="{PoissonWindow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/PoissonWindow.html}", note=[Accessed: 11-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_poissonwindow, organization={Wolfram Research}, title={PoissonWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/PoissonWindow.html}, note=[Accessed: 11-August-2025]}