Documentation

nuttallwin

Nuttall-defined minimum 4-term Blackman-Harris window

Syntax

w = nuttallwin(N)
w = nuttallwin(N,SFLAG)

Description

w = nuttallwin(N) returns a Nuttall defined N-point, 4-term symmetric Blackman-Harris window in the column vector w. The window is minimum in the sense that its maximum sidelobes are minimized. The coefficients for this window differ from the Blackman-Harris window coefficients computed with blackmanharris and produce slightly lower sidelobes.

w = nuttallwin(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 Algorithms.

Examples

collapse all

Compare 64-point Nuttall and Blackman-Harris windows. Plot them using wvtool.

L = 64;
w = blackmanharris(L);
y = nuttallwin(L);
wvtool(w,y) Compute the maximum difference between the two windows.

max(abs(y-w))
ans = 0.0099

Algorithms

The equation for the symmetric Nuttall defined four-term Blackman-Harris window is

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

where n= 0,1,2, ... N-1.

The equation for the periodic Nuttall defined four-term Blackman-Harris window is

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

where n= 0,1,2, ... N-1. The periodic window is N-periodic.

The coefficients for this window are

a0 = 0.3635819

a1 = 0.4891775

a2 = 0.1365995

a3 = .0106411

References

 Nuttall, Albert H. “Some Windows with Very Good Sidelobe Behavior.” IEEE® Transactions on Acoustics, Speech, and Signal Processing. Vol. ASSP-29, February 1981, pp. 84–91.