represents a Welch window function of x.


uses the parameter α.



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Basic Examples  (3)

Shape of a 1D Welch window:

Shape of a 2D Welch window:

Extract the continuous function representing the Welch window:

Parameterized Welch window:

Scope  (6)

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

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

Translated and dilated Welch window:

2D Welch window with a circular support:

Evaluate numerically:

Discrete Welch window of length 15:

Discrete 15×10 2D Welch window:

Applications  (3)

Create a moving-average filter of length 11:

Smooth the filter using a Welch 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 the 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 Welch window:

Normalize to create a window with unit area:

Fourier transform of the Welch window:

Power spectrum of the Welch window:

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:

Use a pure function instead:

Introduced in 2012