WOLFRAM

represents a HannPoisson window function of x.

uses the parameter α.

Details

Examples

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Basic Examples  (3)Summary of the most common use cases

Shape of a 1D HannPoisson window:

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Shape of a 2D HannPoisson window:

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Extract the continuous function representing the HannPoisson window:

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Parameterized HannPoisson window:

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

Evaluate numerically:

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Shape of a 1D HannPoisson window using a specified parameter:

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

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Translated and dilated HannPoisson window:

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2D HannPoisson window with a circular support:

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Discrete HannPoisson window of length 15:

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Discrete 15×10 2D HannPoisson window:

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Applications  (3)Sample problems that can be solved with this function

Create a moving average filter of length 21:

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Taper the filter using a Hamming window:

Log-magnitude plot of the power spectra of the filters:

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Use a window specification to calculate sample PowerSpectralDensity:

Calculate the spectrum:

Compare to spectral density calculated without a windowing function:

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The plot shows that window smooths the spectral density:

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Compare to the theoretical spectral density of the process:

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Use a window specification for time series estimation:

Specify window for spectral estimator:

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Properties & Relations  (3)Properties of the function, and connections to other functions

HannPoissonWindow[x,0] is equivalent to a Hann window:

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The area under the HannPoisson window:

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Normalize to create a window with unit area:

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Fourier transform of the HannPoisson window:

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Power spectrum of the HannPoisson window:

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Possible Issues  (1)Common pitfalls and unexpected behavior

2D sampling of HannPoisson window will use a different parameter for each row of samples when passed as a symbol to Array:

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Use a pure function instead:

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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.

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 ]}

@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 ]}

@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 ]}