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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

expand all

### Blackman Window

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:

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

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 nN-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.