represents a Nuttall window function of x.


  • NuttallWindow 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.
  • NuttallWindow[x] is equal to  (121849 cos(2 pi x)+36058 cos(4 pi x)+3151 cos(6 pi x)+88942)/(250000) -1/2<=x<=1/2; 0 TemplateBox[{x}, Abs]>1/2; .
  • NuttallWindow automatically threads over lists.


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Basic Examples  (3)

Shape of a 1D Nuttall window:

Shape of a 2D Nuttall window:

Extract the continuous function representing the Nuttall window:

Scope  (4)

Evaluate numerically:

Translated and dilated Nuttall window:

2D Nuttall window with a circular support:

Discrete Nuttall window of length 15:

Discrete 15×10 2D Nuttall window:

Applications  (3)

Create a moving-average filter of length 21:

Taper the filter using a Nuttall 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 Nuttall window:

Normalize to create a window with unit area:

Fourier transform of the Nuttall window:

Power spectrum of the Nuttall window:

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


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


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


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


@misc{reference.wolfram_2024_nuttallwindow, author="Wolfram Research", title="{NuttallWindow}", year="2012", howpublished="\url{}", note=[Accessed: 20-July-2024 ]}


@online{reference.wolfram_2024_nuttallwindow, organization={Wolfram Research}, title={NuttallWindow}, year={2012}, url={}, note=[Accessed: 20-July-2024 ]}