# sigwin.nuttallwin class

Package: sigwin

Construct Nuttall defined 4–term Blackman-Harris window object

## Description

 Note:   The use of `sigwin.nuttallwin` is not recommended. Use `nuttallwin` instead.

`sigwin.nuttallwin` creates a handle to a Nuttall defined 4–term Blackman-Harris window object for use in spectral analysis and FIR filtering by the window method. Object methods enable workspace import and ASCII file export of the window values.

## Construction

`H = sigwin.nuttallwin` returns a Nuttall defined 4–term Blackman-Harris window object window object `H` of length 64.

`H = sigwin.nuttallwin(Length)` returns a Nuttall defined 4–term Blackman-Harris window object `H` of length `Length`. Entering a positive noninteger value for `Length` rounds the length to the nearest integer. Entering a 1 for `Length` results in a window with a single value of 1. The `SamplingFlag` property defaults to `'symmetric'`.

## Properties

 `Length` Nuttall defined 4–term Blackman-Harris window length. The window length must be a positive integer. Entering a positive noninteger value for `Length` rounds the length to the nearest integer. Entering a 1 for `Length` results in a window with a single value of 1. `SamplingFlag` The type of window returned as one of `'symmetric'` or `'periodic'`. The default is `'symmetric'`. A symmetric window exhibits perfect symmetry between halves of the window. Setting the `SamplingFlag` property to `'periodic'` results in a N-periodic window. The equations for the Nuttall defined 4–term Blackman-Harris window differ slightly based on the value of the `SamplingFlag` property. See Definitions for details.

## Methods

 generate Generates Nuttall defined 4–term Blackman-Harris window info Display information about Nuttall defined 4–term Blackman-Harris window object winwrite Save Nuttall defined 4-term Blackman-Harris window object values in ASCII file

## Definitions

The following equation defines the symmetric Nuttall defined 4–term Blackman-Harris window of length `N`.

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

The following equation defines the periodic Nuttall defined 4–term Blackman-Harris window of length `N`.

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

The following table lists the coefficients:

CoefficientValue
`a0`0.3635819
`a1`0.4891775
`a2`0.1365995
`a3`0.0106411

## Copy Semantics

Handle. To learn how copy semantics affect your use of the class, see Copying Objects in the MATLAB® Programming Fundamentals documentation.

## Examples

Construct a length `N = 64` symmetric Nuttall defined 4–term Blackman-Harris window:

```H = sigwin.nuttallwin; wvtool(H)```

Generate a length `N = 128` periodic Nuttall defined 4-term Blackman-Harris window, return values, and write ASCII file:

```H = sigwin.nuttallwin(128); H.SamplingFlag = 'periodic'; % Return window with generate win = generate(H); % Write ASCII file in current directory % with window values winwrite(H,'nuttallwin_128')```

## References

Nuttall, A. H. "Some Windows with Very Good Sidelobe Behavior." IEEE® Transactions on Acoustics, Speech, and Signal Processing. Vol. 29, 1981, pp. 84–91.