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# sigwin.blackman class

Package: sigwin

Construct Blackman window object

## Description

sigwin.blackman creates a handle to a Blackman 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.

The following equation defines the Blackman window of length N:

$w\left(n\right)=0.42-0.5\mathrm{cos}\left(2\pi n/\left(N-1\right)\right)+0.08\mathrm{cos}\left(4\pi n/\left(N-1\right)\right)\text{ }0\le n\le M-1$

where M is N/2 for N even and (N+1)/2 for N odd.

In the symmetric case, the second half of the Blackman window $M\le n\le N-1$ is obtained by flipping the first half around the midpoint. The symmetric option is the preferred method when using a Blackman window in FIR filter design.

The periodic Blackman window is constructed by extending the desired window length by one sample to N+1, constructing a symmetric window, and removing the last sample. The periodic version is the preferred method when using a Blackman window in spectral analysis because the discrete Fourier transform assumes periodic extension of the input vector.

## Construction

H = sigwin.blackman returns a Blackman window object H of length 64 with symmetric sampling.

H = sigwin.blackman(Length) returns a Blackman window object H of length Length with symmetric sampling. Length requires 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.

H = sigwin.blackman(Length,SamplingFlag) returns a Blackman window object H with sampling Sampling_Flag. The Sampling_Flag can be either 'symmetric' or 'periodic'.

## Properties

 Length Blackman 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 'symmetric' is the default and forces exact symmetry between the first and second halves of the Blackman window. A symmetric window is preferred in FIR filter design by the window method. 'periodic' designs a symmetric Blackman window of length Length+1 and truncates the window to length Length. This design is preferred in spectral analysis where the window is treated as one period of a Length-point periodic sequence.

## Methods

 generate Generates Blackman window info Display information about Blackman window object winwrite Save Blackman window in ASCII file

## Copy Semantics

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

## Examples

Default length N=64 symmetric Blackman window:

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

Generate length N=128 periodic Blackman window, return values, and write ASCII file:

```H = sigwin.blackman(128,'periodic');
% Return window with generate
win = generate(H);
% Write ASCII file in current directory
% with window values
winwrite(H,'blackman_128')```

## References

Oppenheim, A.V. and Schafer, R.W. Discrete-time Signal Processing, Upper Saddle River, N.J: Prentice Hall, 1989, pp. 444–447.