Shape of a 1D cosine window:

Shape of a 2D cosine window:

Extract the continuous function representing the cosine window:

Parameterized cosine window:

Evaluate numerically:

Shape of a 1D cosine window using a specified exponent:

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

Translated and dilated cosine window:

2D cosine window with a circular support:

Discrete cosine window of length 15:

Discrete 15×10 2D cosine window:

Create a moving-average filter of length 11:

Taper the filter using a cosine window:

Log-magnitude plot of the power spectra of the two 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 the window for the spectral estimator:

CosineWindow[x,0] is equivalent to a Dirichlet window:

The area under the cosine window:

Normalize to create a window with unit area:

Fourier transform of the cosine window:

Power spectrum of the cosine window:

2D sampling of cosine window uses a different exponent for each row of samples when passed as a symbol to Array:

Use a pure function instead: