FlatTopWindow

FlatTopWindow[x]

represents an exact flat top window function of x.

Details

  • FlatTopWindow 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.
  • FlatTopWindow[x] is equal to  (416631580 cos(2 pi x)+277263158 cos(4 pi x)+83578947 cos(6 pi x)+6947368 cos(8 pi x)+215578948)/(1000000000) -1/2<=x<=1/2; 0 TemplateBox[{x}, Abs]>1/2; .
  • FlatTopWindow automatically threads over lists.

Examples

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Basic Examples  (3)

Shape of a 1D exact flat top window:

Shape of a 2D exact flat top window:

Extract the continuous function representing the exact flat top window:

Scope  (4)

Evaluate numerically:

Translated and dilated exact flat top window:

2D exact flat top window with a circular support:

Discrete exact flat top window of length 15:

Discrete 15×10 2D flat top window:

Applications  (3)

Create a moving average filter of length 21:

Taper the filter using a flat top 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 exact flat top window:

Normalize to create a window with unit area:

Fourier transform of the exact flat top window:

Power spectrum of the exact flat top window:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_flattopwindow, author="Wolfram Research", title="{FlatTopWindow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/FlatTopWindow.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_flattopwindow, organization={Wolfram Research}, title={FlatTopWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/FlatTopWindow.html}, note=[Accessed: 21-February-2025 ]}