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Nuttall-defined minimum 4-term Blackman-Harris window

`w = nuttallwin(N)`

w = nuttallwin(N,SFLAG)

returns a Nuttall defined `w`

= nuttallwin(`N`

)`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.

uses `w`

= nuttallwin(N,`SFLAG`

)`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.

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

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

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

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

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

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

The coefficients for this window are

a_{0} = 0.3635819

a_{1} = 0.4891775

a_{2} = 0.1365995

a_{3} = 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.

`barthannwin`

|`bartlett`

|`blackmanharris`

|`bohmanwin`

|`parzenwin`

|`rectwin`

|`triang`

| WVTool