BartlettHannWindow

BartlettHannWindow[x]

represents a Bartlett–Hann window function of x.

Details

  • BartlettHannWindow 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.
  • BartlettHannWindow[x] is equal to  (31)/(50)-(12 x)/(25)+(19)/(50) cos(2 pi x) 0<=x<=1/2; (31)/(50)+(12 x)/(25)+(19)/(50) cos(2 pi x) -1/2<=x<0; 0 TemplateBox[{x}, Abs]>1/2; .
  • BartlettHannWindow automatically threads over lists.

Examples

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Basic Examples  (3)

Shape of a 1D Bartlett–Hann window:

Shape of a 2D Bartlett–Hann window:

Extract the continuous function representing the Bartlett–Hann window:

Scope  (4)

Evaluate numerically:

Translated and dilated Bartlett–Hann window:

2D Bartlett–Hann window with a circular support:

Discrete Bartlett–Hann window of length 15:

Discrete 15×10 2D Bartlett–Hann window:

Applications  (3)

Create a moving average filter of length 11:

Smooth the filter using a Bartlett–Hann window:

Log-magnitude plot of the frequency spectrum 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 Bartlett–Hann window:

Normalize to create a window with unit area:

Fourier transform of the Bartlett–Hann window:

Power spectrum of the Bartlett–Hann window:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_bartletthannwindow, author="Wolfram Research", title="{BartlettHannWindow}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/BartlettHannWindow.html}", note=[Accessed: 22-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_bartletthannwindow, organization={Wolfram Research}, title={BartlettHannWindow}, year={2012}, url={https://reference.wolfram.com/language/ref/BartlettHannWindow.html}, note=[Accessed: 22-February-2025 ]}