Shape of a 1D Tukey window:

Shape of a 2D Tukey window:

Extract the continuous function representing the Tukey window:

Parameterized Tukey window:

Evaluate numerically:

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

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

Translated and dilated Tukey window:

2D Tukey window with a circular support:

Discrete Tukey window of length 15:

Discrete 15×10 2D Tukey window:

Use the Tukey window to diminish the effect of signal partitioning when computing the spectrogram:

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:

TukeyWindow[x,1] is equivalent to a Hann window:

TukeyWindow[x,0] is equivalent to a box window:

TukeyWindow[x,1] is equivalent to a Hann window:

Tukey window is a convolution of a unit pulse with a raised cosine:

The area under the Tukey window:

Normalize to create a window with unit area:

Fourier transform of the Tukey window:

Power spectrum of the Tukey window:

Fourier transform of the parametrized Tukey window:

Variation of the magnitude spectrum of the Tukey window as a function of the parameter :

Discrete-time Fourier transform of the discrete Tukey window of length 11:

Magnitude at ω=0:

Magnitude spectrum:

Power spectra for three different window lengths:

Power spectra for three different values of the shape parameter :

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

Use a pure function instead: