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# sigwin.nuttallwin class

Package: sigwin

Construct Nuttall defined 4–term Blackman-Harris window object

## Description

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.

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

The following table lists the coefficients:

CoefficientValue
a00.3635819
a10.4891775
a20.1365995
a30.0106411

## 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.