represents a Cauchy window function of x.
uses the parameter α.
- CauchyWindow, also known as the Abel window, 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.
- CauchyWindow[x,α] is equal to .
- CauchyWindow[x] is equivalent to CauchyWindow[x,3].
- CauchyWindow automatically threads over lists.
Examplesopen allclose all
Basic Examples (3)
Use a window specification to calculate sample PowerSpectralDensity:
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:
Properties & Relations (3)
CauchyWindow[x,0] is equivalent to a Dirichlet window:
The area under the Cauchy window:
Normalize to create a window with unit area:
Fourier transform of the Cauchy window:
Possible Issues (1)
2D sampling of Cauchy window will use a different parameter for each row of samples when passed as a symbol to Array:
Wolfram Research (2012), CauchyWindow, Wolfram Language function, https://reference.wolfram.com/language/ref/CauchyWindow.html.
Wolfram Language. 2012. "CauchyWindow." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CauchyWindow.html.
Wolfram Language. (2012). CauchyWindow. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CauchyWindow.html