Shape of a 1D Hann–Poisson window:

Shape of a 2D Hann–Poisson window:

Extract the continuous function representing the Hann–Poisson window:

Parameterized Hann–Poisson window:

Evaluate numerically:

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

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

Translated and dilated Hann–Poisson window:

2D Hann–Poisson window with a circular support:

Discrete Hann–Poisson window of length 15:

Discrete 15×10 2D Hann–Poisson window:

Create a moving average filter of length 21:

Taper the filter using a Hamming window:

Log-magnitude plot of the power spectra 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:

HannPoissonWindow[x,0] is equivalent to a Hann window:

The area under the Hann–Poisson window:

Normalize to create a window with unit area:

Fourier transform of the Hann–Poisson window:

Power spectrum of the Hann–Poisson window:

2D sampling of Hann–Poisson window will use a different parameter for each row of samples when passed as a symbol to Array:

Use a pure function instead: