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Nuttall-defined minimum 4-term Blackman-Harris window



w = nuttallwin(L) returns a Nuttall defined L-point, four-term symmetric Blackman-Harris window. The coefficients for this window differ from the Blackman-Harris window coefficients computed with blackmanharris and produce slightly lower sidelobes.

w = nuttallwin(L,sflag) uses sflag window sampling.


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

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

{"String":"Figure Window Visualization Tool contains 2 axes objects and other objects of type uimenu, uitoolbar, uipanel. Axes object 1 with title Time domain contains 2 objects of type line. Axes object 2 with title Frequency domain contains 2 objects of type line.","Tex":["Time domain","Frequency domain"],"LaTex":[]}

Compute the maximum difference between the two windows.

ans = 0.0099

Input Arguments

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Window length, specified as a real positive scalar.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Window sampling, specified as "symmetric" or "periodic". For the equations that define the symmetric and periodic windows, see Algorithms.

Output Arguments

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Nuttall defined Blackman-Harris window, returned as a column vector of length L. The function minimizes the maximum sidelobes of the window.


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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced before R2006a