# Documentation

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# blackman

Blackman window

## Syntax

`w = blackman(N)w = blackman(N,SFLAG)`

## Description

`w = blackman(N)` returns the `N`-point symmetric Blackman window in the column vector `w`, where `N` is a positive integer.

`w = blackman(N,SFLAG)` returns an `N`-point Blackman window using the window sampling specified by `'sflag'`, which can be either `'periodic'` or `'symmetric'` (the default). The `'periodic'` flag is useful for DFT/FFT purposes, such as in spectral analysis. The DFT/FFT contains an implicit periodic extension and the periodic flag enables a signal windowed with a periodic window to have perfect periodic extension. When `'periodic'` is specified, `blackman` computes a length `N+1` window and returns the first `N` points. When using windows for filter design, the `'symmetric'` flag should be used.

See Definitions for a description of the difference between the symmetric and periodic windows.

 Note   If you specify a one-point window (set `N = 1`), the value `1` is returned.

## Examples

collapse all

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

```L = 64; wvtool(blackman(L)) ```

## Definitions

The following equation defines the Blackman window of length N:

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

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

In the symmetric case, the second half of the Blackman window M ≤ n ≤ N – 1 is obtained by flipping 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.