# blackman

Blackman window

## Syntax

w = blackman(L)
w = blackman(L,sflag)

## Description

example

w = blackman(L) returns an L-point symmetric Blackman window.
w = blackman(L,sflag) returns a Blackman window using the window sampling method specified by sflag.

## Examples

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Create a 64-point Blackman window. Display the result using wvtool.

L = 64; wvtool(blackman(L))

## Input Arguments

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Window length, specified as a positive integer.

Data Types: single | double

Window sampling method, specified as:

• 'symmetric' — Use this option when using windows for filter design.

• 'periodic' — This option is useful for spectral analysis because it enables a windowed signal to have the perfect periodic extension implicit in the discrete Fourier transform. When 'periodic' is specified, the function computes a window of length L + 1 and returns the first L points.

## Output Arguments

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Blackman window, returned as a column vector.

## Algorithms

The following equation defines the Blackman window of length N:

$w\left(n\right)=0.42-0.5\mathrm{cos}\left(\frac{2\pi n}{L-1}\right)+0.08\mathrm{cos}\left(\frac{4\pi n}{L-1}\right),\text{ }0\le n\le M-1$

where M is N/2 when N is even and (N + 1)/2 when N is odd.

In the symmetric case, the second half of the Blackman window, M ≤ n ≤ N – 1, is obtained by reflecting the first half around the midpoint. The symmetric option is the preferred method when using a Blackman window in FIR filter design.

The periodic Blackman window is constructed by extending the desired window length by one sample to N + 1, constructing a symmetric window, and removing the last sample. The periodic version is the preferred method when using a Blackman window in spectral analysis because the discrete Fourier transform assumes periodic extension of the input vector.

## References

[1] Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, 1999, pp. 468–471.

## Version History

Introduced before R2006a