# CosineWindow

CosineWindow[x]

represents a cosine window function of x.

CosineWindow[x,α]

uses the exponent α.

# Details • CosineWindow is a window function typically used in signal processing applications where data needs to be processed in short segments.
• Window functions have a smoothing effect by gradually tapering data values to zero at the ends of each segment.
• • CosineWindow[x,α] is equal to for and 0 otherwise.
• CosineWindow[x] is equivalent to CosineWindow[x,1].
• CosineWindow automatically threads over lists.

# Examples

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## Basic Examples(3)

Shape of a 1D cosine window:

Shape of a 2D cosine window:

Extract the continuous function representing the cosine window:

Parameterized cosine window:

## Scope(6)

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:

## Applications(3)

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:

## Properties & Relations(3)

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:

## Possible Issues(1)

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