BohmanWindow

BohmanWindow[x]

represents a Bohman window function of x.

Details

  • BohmanWindow 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.
  • BohmanWindow[x] is equal to  (-sin(2 pi x)+2 pi x cos(2 pi x)+pi cos(2 pi x))/pi -1/2<=x<0; (sin(2 pi x)-2 pi x cos(2 pi x)+pi cos(2 pi x))/pi 0<=x<=1/2; 0 TemplateBox[{x}, Abs]>1/2; .
  • BohmanWindow automatically threads over lists.

Examples

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Basic Examples  (3)

Shape of a 1D Bohman window:

Shape of a 2D Bohman window:

Extract the continuous function representing the Bohman window:

Scope  (4)

Translated and dilated Bohman window:

2D Bohman window with a circular support:

Evaluate numerically:

Discrete Bohman window of length 15:

Discrete 15×10 2D Bohman window:

Applications  (3)

Create a moving-average filter of length 21:

Taper the filter using a Bohman window:

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

Use a window specification to calculate sample PowerSpectralDensity:

Calculate the spectrum:

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:

Use a window specification for time series estimation:

Specify window for spectral estimator:

Properties & Relations  (2)

The area under the Bohman window:

Normalize to create a window with unit area:

Fourier transform of the Bohman window:

Power spectrum of the Bohman window:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_bohmanwindow, author="Wolfram Research", title="{BohmanWindow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/BohmanWindow.html}", note=[Accessed: 22-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_bohmanwindow, organization={Wolfram Research}, title={BohmanWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/BohmanWindow.html}, note=[Accessed: 22-February-2025 ]}