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Nuttall-defined minimum 4-term Blackman-Harris window


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


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.


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

L = 64;
w = blackmanharris(L);
y = nuttallwin(L);

Compute the maximum difference between the two windows.

ans = 0.0099


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


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

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


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 = 0.0106411


[1] 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.

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