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# blackmanharris

Minimum 4-term Blackman-Harris window

## Syntax

w = blackmanharris(N)
w = blackmanharris(N,SFLAG)

## Description

w = blackmanharris(N) returns an N-point symmetric 4-term Blackman-Harris window in the column vector w. The window is minimum in the sense that its maximum sidelobes are minimized.

w = blackmanharris(N,SFLAG) uses SFLAG window sampling. SFLAG can be 'symmetric' or 'periodic'. The default is 'symmetric'. You can find the equations defining the symmetric and periodic windows in Definitions.

## Examples

expand all

### Blackman-Harris Window

Create a 32-point symmetric Blackman-Harris window. Display the result using wvtool.

```N = 32;
wvtool(blackmanharris(N))
```

## Definitions

The equation for the symmetric 4-term Blackman-harris window of length N is

$w\left(n\right)={a}_{0}-{a}_{1}\mathrm{cos}\left(\frac{2\pi n}{N-1}\right)+{a}_{2}\mathrm{cos}\left(\frac{4\pi n}{N-1}\right)-{a}_{3}\mathrm{cos}\left(\frac{6\pi n}{N-1}\right)\text{ }0\le n\le N-1$

The equation for the periodic 4-term Blackman-harris window of length N is

$w\left(n\right)={a}_{0}-{a}_{1}\mathrm{cos}\left(\frac{2\pi n}{N}\right)+{a}_{2}\mathrm{cos}\left(\frac{4\pi n}{N}\right)-{a}_{3}\mathrm{cos}\left(\frac{6\pi n}{N}\right)\text{ }0\le n\le N-1$

The periodic window is N-periodic.

The following table lists the coefficients:

CoefficientValue
a00.35875
a10.48829
a20.14128
a30.01168

## References

[1] Harris, Fredric J. "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform." Proceedings of the IEEE®. Vol. 66, January 1978, pp. 51–83.