represents a Hamming window function of x.


  • HammingWindow is a window function typically used for pulse shaping in telecommunication applications as well as for finite impulse response (FIR) filter design and spectral analysis.
  • Window functions are used in applications where data is processed in short segments and have a smoothing effect by gradually tapering data values to zero at the ends of each segment.
  • HammingWindow[x] is equal to  (21)/(46) cos(2 pi x)+(25)/(46) -1/2<=x<=1/2; 0 TemplateBox[{x}, Abs]>1/2; .
  • HammingWindow automatically threads over lists.


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Basic Examples  (3)

Shape of a 1D Hamming window:

Shape of a 2D Hamming window:

Extract the continuous function representing the Hamming window:

Scope  (4)

Evaluate numerically:

Translated and dilated Hamming window:

2D Hamming window with a circular support:

Discrete Hamming window of length 15:

Discrete 15×10 2D Hamming window:

Applications  (3)

Create a moving average filter of length 21:

Taper the filter using a Hamming 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  (4)

The area under the Hamming window:

Normalize to create a window with unit area:

Fourier transform of the Hamming window:

Power spectrum of the Hamming window:

Discrete-time Fourier transform of the discrete Hamming window of length 11:

Magnitude at ω=0:

Magnitude spectrum:

Power spectra of the Hamming and rectangular windows:

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


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


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


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


@misc{reference.wolfram_2024_hammingwindow, author="Wolfram Research", title="{HammingWindow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/HammingWindow.html}", note=[Accessed: 17-July-2024 ]}


@online{reference.wolfram_2024_hammingwindow, organization={Wolfram Research}, title={HammingWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/HammingWindow.html}, note=[Accessed: 17-July-2024 ]}