represents a BlackmanNuttall window function of x.


  • BlackmanNuttallWindow 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.
  • BlackmanNuttallWindow[x] is equal to  (4891775 cos(2 pi x)+1365995 cos(4 pi x)+106411 cos(6 pi x)+3635819)/(10000000) -1/2<=x<=1/2; 0 TemplateBox[{x}, Abs]>1/2; .
  • BlackmanNuttallWindow automatically threads over lists.


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Basic Examples  (3)

Shape of a 1D BlackmanNuttall window:

Shape of a 2D BlackmanNuttall window:

Extract the continuous function representing the BlackmanNuttall window:

Scope  (4)

Evaluate numerically:

Translated and dilated BlackmanNuttall window:

2D BlackmanNuttall window with a circular support:

Discrete BlackmanNuttall window of length 15:

Discrete 15×10 2D BlackmanNuttall window:

Applications  (3)

Create a moving average filter of length 11:

Taper the filter using a BlackmanNuttall 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 BlackmanNuttall window:

Normalize to create a window with unit area:

Fourier transform of the BlackmanNuttall window:

Power spectrum of the BlackmanNuttall window:

Wolfram Research (2012), BlackmanNuttallWindow, Wolfram Language function,


Wolfram Research (2012), BlackmanNuttallWindow, Wolfram Language function,


Wolfram Language. 2012. "BlackmanNuttallWindow." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2012). BlackmanNuttallWindow. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_blackmannuttallwindow, author="Wolfram Research", title="{BlackmanNuttallWindow}", year="2012", howpublished="\url{}", note=[Accessed: 21-May-2024 ]}


@online{reference.wolfram_2024_blackmannuttallwindow, organization={Wolfram Research}, title={BlackmanNuttallWindow}, year={2012}, url={}, note=[Accessed: 21-May-2024 ]}