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DirichletWindow[x]

represents a Dirichlet window function of x.

Details
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Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
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DirichletWindow

DirichletWindow[x]

represents a Dirichlet window function of x.

Details

  • DirichletWindow, also known as the rectangular or boxcar window, is a window function used in signal processing applications where data needs to be processed in short segments.
  • DirichletWindow[x] is equal to  1 -1/2<=x<=1/2; 0 TemplateBox[{x}, Abs]>1/2; .
  • DirichletWindow automatically threads over lists.

Examples

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Basic Examples  (3)

Shape of a 1D Dirichlet window:

Shape of a 2D Dirichlet window:

Extract the continuous function representing the Dirichlet window:

Scope  (4)

Evaluate numerically:

Translated and dilated Dirichlet window:

2D Dirichlet window with a circular support:

Discrete Dirichlet window of length 15:

Discrete 15×10 2D Dirichlet window:

Applications  (2)

Use a window specification to calculate sample PowerSpectralDensity:

Calculate the spectrum:

Compare to spectral density calculated without a windowing function:

The Dirichlet window does not change the spectral density:

Compare to the theoretical spectral density of the process:

Use a window specification for time series estimation:

Specify the window for the spectral estimator:

Properties & Relations  (3)

DirichletWindow is equivalent to UnitBox:

Fourier transform of the Dirichlet window:

Power spectrum of the Dirichlet window:

Discrete-time Fourier transform of the discrete Dirichlet window of length 11:

Magnitude at ω=0:

Power spectrum:

Wolfram Research (2012), DirichletWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/DirichletWindow.html.

Text

Wolfram Research (2012), DirichletWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/DirichletWindow.html.

CMS

Wolfram Language. 2012. "DirichletWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DirichletWindow.html.

APA

Wolfram Language. (2012). DirichletWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DirichletWindow.html

BibTeX

@misc{reference.wolfram_2025_dirichletwindow, author="Wolfram Research", title="{DirichletWindow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/DirichletWindow.html}", note=[Accessed: 10-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_dirichletwindow, organization={Wolfram Research}, title={DirichletWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/DirichletWindow.html}, note=[Accessed: 10-August-2025]}