HannPoissonWindow
✖
HannPoissonWindow
Details

- HannPoissonWindow 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.
- HannPoissonWindow[x,α] is equal to
.
- HannPoissonWindow[x] is equivalent to HannPoissonWindow[x,1].
- HannPoissonWindow automatically threads over lists.

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

https://wolfram.com/xid/0rkt7ijm1lluqhe-55nvy5

Shape of a 2D Hann–Poisson window:

https://wolfram.com/xid/0rkt7ijm1lluqhe-yyuiog

Extract the continuous function representing the Hann–Poisson window:

https://wolfram.com/xid/0rkt7ijm1lluqhe-i5bqnh

Parameterized Hann–Poisson window:

https://wolfram.com/xid/0rkt7ijm1lluqhe-zwjlmu

Scope (6)Survey of the scope of standard use cases

https://wolfram.com/xid/0rkt7ijm1lluqhe-rfdjbb

Shape of a 1D Hann–Poisson window using a specified parameter:

https://wolfram.com/xid/0rkt7ijm1lluqhe-y9d2xu

Variation of the shape as a function of the parameter α:

https://wolfram.com/xid/0rkt7ijm1lluqhe-eu37ay

Translated and dilated Hann–Poisson window:

https://wolfram.com/xid/0rkt7ijm1lluqhe-fzqpy6

2D Hann–Poisson window with a circular support:

https://wolfram.com/xid/0rkt7ijm1lluqhe-h4a5s3

Discrete Hann–Poisson window of length 15:

https://wolfram.com/xid/0rkt7ijm1lluqhe-5yhlc9

Discrete 15×10 2D Hann–Poisson window:

https://wolfram.com/xid/0rkt7ijm1lluqhe-ivcfcj

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

https://wolfram.com/xid/0rkt7ijm1lluqhe-b4svbb

Taper the filter using a Hamming window:

https://wolfram.com/xid/0rkt7ijm1lluqhe-1k06dy
Log-magnitude plot of the power spectra of the filters:

https://wolfram.com/xid/0rkt7ijm1lluqhe-65dzhv

Use a window specification to calculate sample PowerSpectralDensity:

https://wolfram.com/xid/0rkt7ijm1lluqhe-la7hx0

https://wolfram.com/xid/0rkt7ijm1lluqhe-xvpxo9
Compare to spectral density calculated without a windowing function:

https://wolfram.com/xid/0rkt7ijm1lluqhe-012m6s

https://wolfram.com/xid/0rkt7ijm1lluqhe-phnp33

The plot shows that window smooths the spectral density:

https://wolfram.com/xid/0rkt7ijm1lluqhe-z97d2x

Compare to the theoretical spectral density of the process:

https://wolfram.com/xid/0rkt7ijm1lluqhe-2bqb4v

Use a window specification for time series estimation:

https://wolfram.com/xid/0rkt7ijm1lluqhe-8tceex
Specify window for spectral estimator:

https://wolfram.com/xid/0rkt7ijm1lluqhe-nkbyb7

Properties & Relations (3)Properties of the function, and connections to other functions
HannPoissonWindow[x,0] is equivalent to a Hann window:

https://wolfram.com/xid/0rkt7ijm1lluqhe-vfnwv2

The area under the Hann–Poisson window:

https://wolfram.com/xid/0rkt7ijm1lluqhe-bvk48s

Normalize to create a window with unit area:

https://wolfram.com/xid/0rkt7ijm1lluqhe-uvswua

Fourier transform of the Hann–Poisson window:

https://wolfram.com/xid/0rkt7ijm1lluqhe-hw628m

Power spectrum of the Hann–Poisson window:

https://wolfram.com/xid/0rkt7ijm1lluqhe-6mml6t

Possible Issues (1)Common pitfalls and unexpected behavior
2D sampling of Hann–Poisson window will use a different parameter for each row of samples when passed as a symbol to Array:

https://wolfram.com/xid/0rkt7ijm1lluqhe-0oh59a


https://wolfram.com/xid/0rkt7ijm1lluqhe-iqrxnt

Wolfram Research (2012), HannPoissonWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/HannPoissonWindow.html.
Text
Wolfram Research (2012), HannPoissonWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/HannPoissonWindow.html.
Wolfram Research (2012), HannPoissonWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/HannPoissonWindow.html.
CMS
Wolfram Language. 2012. "HannPoissonWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HannPoissonWindow.html.
Wolfram Language. 2012. "HannPoissonWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HannPoissonWindow.html.
APA
Wolfram Language. (2012). HannPoissonWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HannPoissonWindow.html
Wolfram Language. (2012). HannPoissonWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HannPoissonWindow.html
BibTeX
@misc{reference.wolfram_2025_hannpoissonwindow, author="Wolfram Research", title="{HannPoissonWindow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/HannPoissonWindow.html}", note=[Accessed: 06-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_hannpoissonwindow, organization={Wolfram Research}, title={HannPoissonWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/HannPoissonWindow.html}, note=[Accessed: 06-June-2025
]}