Shape of a 1D Parzen window:

Shape of a 2D Parzen window:

Extract the continuous function representing the Parzen window:

Evaluate numerically:

Translated and dilated Parzen window:

2D Parzen window with a circular support:

Discrete Parzen window of length 15:

Discrete 15×11 2D Parzen window:

Decrease the size of an image by a factor of 5 using the Parzen method:

Create a moving-average filter of length 21:

Taper the filter using a Parzen 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:

The area under the Parzen window:

Normalize to create a window with unit area:

Fourier transform of the Parzen window:

Power spectrum of the Parzen window: