DirichletWindow [x]
represents a Dirichlet window function of x.
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 [画像: 1 -1/2<=x<=1/2; 0 TemplateBox[{x}, Abs]>1/2; ].
- DirichletWindow automatically threads over lists.
![画像: 1 -1/2<=x<=1/2; 0 TemplateBox[{x}, Abs]>1/2;](/index.cgi/contrast/https://reference.wolfram.com/language/ref/Files/DirichletWindow.en/2.png){kind=link}
Examples
open all close allBasic 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:
See Also
Related Guides
History
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: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_dirichletwindow, organization={Wolfram Research}, title={DirichletWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/DirichletWindow.html}, note=[Accessed: 04-January-2026]}