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FlatTopWindow
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FlatTopWindow

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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)Summary of the most common use cases

Shape of a 1D exact flat top window:

In[1]:=1
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https://wolfram.com/xid/0btnh636hn5u-55nvy5
Out[1]=1

Shape of a 2D exact flat top window:

In[1]:=1
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https://wolfram.com/xid/0btnh636hn5u-yyuiog
Out[1]=1

Extract the continuous function representing the exact flat top window:

In[1]:=1
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https://wolfram.com/xid/0btnh636hn5u-i5bqnh
Out[1]=1

Scope  (4)Survey of the scope of standard use cases

Evaluate numerically:

In[1]:=1
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https://wolfram.com/xid/0btnh636hn5u-rfdjbb
Out[1]=1

Translated and dilated exact flat top window:

In[1]:=1
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https://wolfram.com/xid/0btnh636hn5u-fzqpy6
Out[1]=1

2D exact flat top window with a circular support:

In[1]:=1
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https://wolfram.com/xid/0btnh636hn5u-h4a5s3
Out[1]=1

Discrete exact flat top window of length 15:

In[1]:=1
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https://wolfram.com/xid/0btnh636hn5u-5yhlc9
Out[1]=1

Discrete 15×10 2D flat top window:

In[2]:=2
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https://wolfram.com/xid/0btnh636hn5u-ivcfcj
Out[2]=2

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

Create a moving average filter of length 21:

In[2]:=2
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https://wolfram.com/xid/0btnh636hn5u-b4svbb
Out[2]=2

Taper the filter using a flat top window:

In[6]:=6
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https://wolfram.com/xid/0btnh636hn5u-1k06dy

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

In[8]:=8
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https://wolfram.com/xid/0btnh636hn5u-65dzhv
Out[8]=8

Use a window specification to calculate sample PowerSpectralDensity:

In[1]:=1
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https://wolfram.com/xid/0btnh636hn5u-la7hx0

Calculate the spectrum:

In[2]:=2
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https://wolfram.com/xid/0btnh636hn5u-xvpxo9

Compare to spectral density calculated without a windowing function:

In[3]:=3
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https://wolfram.com/xid/0btnh636hn5u-012m6s
In[4]:=4
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https://wolfram.com/xid/0btnh636hn5u-phnp33
Out[4]=4

The plot shows that window smooths the spectral density:

In[5]:=5
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https://wolfram.com/xid/0btnh636hn5u-z97d2x
Out[5]=5

Compare to the theoretical spectral density of the process:

In[6]:=6
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https://wolfram.com/xid/0btnh636hn5u-2bqb4v
Out[6]=6

Use a window specification for time series estimation:

In[1]:=1
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https://wolfram.com/xid/0btnh636hn5u-8tceex

Specify window for spectral estimator:

In[2]:=2
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https://wolfram.com/xid/0btnh636hn5u-nkbyb7
Out[2]=2

Properties & Relations  (2)Properties of the function, and connections to other functions

The area under the exact flat top window:

In[1]:=1
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https://wolfram.com/xid/0btnh636hn5u-bvk48s
Out[1]=1

Normalize to create a window with unit area:

In[2]:=2
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https://wolfram.com/xid/0btnh636hn5u-uvswua
Out[2]=2

Fourier transform of the exact flat top window:

In[1]:=1
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https://wolfram.com/xid/0btnh636hn5u-hw628m
Out[1]=1

Power spectrum of the exact flat top window:

In[2]:=2
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https://wolfram.com/xid/0btnh636hn5u-6mml6t
Out[2]=2
Wolfram Research (2012), FlatTopWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/FlatTopWindow.html.
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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.

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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.

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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

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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: 10-July-2025 ]}

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@misc{reference.wolfram_2025_flattopwindow, author="Wolfram Research", title="{FlatTopWindow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/FlatTopWindow.html}", note=[Accessed: 10-July-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: 10-July-2025 ]}

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@online{reference.wolfram_2025_flattopwindow, organization={Wolfram Research}, title={FlatTopWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/FlatTopWindow.html}, note=[Accessed: 10-July-2025 ]}