represents a Hann window function of x.


uses the parameter α.



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Basic Examples  (3)

Shape of a 1D Hann window:

Shape of a 2D Hann window:

Extract the continuous function representing the Hann window:

Parameterized Hann window:

Scope  (6)

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

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

Translated and dilated Hann window:

2D Hann window with a circular support:

Evaluate numerically:

Discrete Hann window of length 15:

Discrete 15×10 2D Hann window:

Applications  (3)

Create a moving average filter of length 11:

Smooth the filter using a 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  (3)

HannWindow[x,1] is equivalent to a Dirichlet window:

The area under the Hann window:

Normalize to create a window with unit area:

Fourier transform of the Hann window:

Power spectrum of the Hann window:

Possible Issues  (1)

2D sampling of Hann 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