represents a Welch window function of x.
uses the parameter α.
- WelchWindow is a window function typically used for antialiasing and resampling.
- 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.
- WelchWindow[x,α] is equal to .
- WelchWindow[x] is equivalent to WelchWindow[x,1].
- WelchWindow automatically threads over lists.
Examplesopen allclose all
Basic Examples (3)
Create a moving-average filter of length 11:
Taper the filter using a Welch window:
Log-magnitude plot of the power spectra of the filters:
Use a window specification to calculate sample PowerSpectralDensity:
Compare to spectral density calculated without a windowing function:
The plot shows that the window smooths the spectral density:
Compare to the theoretical spectral density of the process:
Use a window specification for time series estimation:
Properties & Relations (2)
Possible Issues (1)
2D sampling of Welch window will use a different parameter for each row of samples when passed as a symbol to Array:
Wolfram Research (2012), WelchWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/WelchWindow.html.
Wolfram Language. 2012. "WelchWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WelchWindow.html.
Wolfram Language. (2012). WelchWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WelchWindow.html