CauchyWindow

CauchyWindow[x]

represents a Cauchy window function of x.

CauchyWindow[x,α]

uses the parameter α.

Details

Examples

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Basic Examples  (3)

Shape of a 1D Cauchy window:

Shape of a 2D Cauchy window:

Extract the continuous function representing the Cauchy window:

Parameterized Cauchy window:

Scope  (6)

Shape of a 1D Cauchy window using a specified parameter:

Variation of the shape as a function of the parameter α:

Translated and dilated Cauchy window:

2D Cauchy window with a circular support:

Evaluate numerically:

Discrete Cauchy window of length 15:

Discrete 15×10 2D Cauchy window:

Applications  (3)

Create a moving average filter of length 11:

Smooth the filter using a Cauchy 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  (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:

Power spectrum 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:

Use a pure function instead:

Introduced in 2012
 (9.0)