# nuttallwin

Nuttall-defined minimum 4-term Blackman-Harris window

## Syntax

w = nuttallwin(L)
w = nuttallwin(L,sflag)

## Description

example

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.

## 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 

## Input Arguments

collapse all

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

collapse all

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

## 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 = 0.0106411

 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.