# GBLACKMAN

## Purpose:

Generates a 3 term Blackman Window.

## Syntax:

GBLACKMAN(N, spacing, "sym")

N

-

An integer, the number of points to generate.

spacing

-

A real, the spacing (delta x) between points.

"sym"

-

Optional. A string, the symmetry flag.

 "symmetric" : Starting and ending points are equal (default). "periodic" : Periodically extended window. Conforms to ISO standard. "iso" : Same as "periodic".

A series.

## Example:

W1: gblackman(100, .01)

generates a 100-point symmetric 3 term Blackman window using the following formula:

where n is the nth point (1 <= n <= N) and N is 100, the number of points. The spacing between samples is set to 0.01.

## Example:

W2: gblackman(100, 0.01, "periodic")

Creates a 100 point periodic Blackman window that conforms to the ISO 18431-1 standard.

where n is the nth point (1 <= n <= N) and N is the number of points to generate. The spacing between samples is set to 0.01.

## Remarks:

The "sym" flag controls the window symmetry as follows:

"Symmetric" sets the last point to be the same value as the first point. For an N point symmetric window, a N-1 point periodic window is effectively created and the Nth point is set to the same value as the first point.

"Periodic" or "iso" creates a periodic window function useful in spectrum analysis applications. "Periodic" or "iso" conforms to the ISO 18431-1 standard for windowing functions.

The Hamming, Hanning, Flattop and Blackman windows are part of the family of cosine window functions. The ISO 18431-1 standard periodic form of these windowing functions are defined by:

where K is the number of window coefficients and N is the length of the window. The symmetric form of the window can be constructed by setting N to N-1.

For the Blackman window:

Use the BLACKMAN function command to automatically create and multiply a Blackman window with a series. For example:

blackman(W1)

multiplies Window 1 with a Blackman window of the same length and spacing as the series in W1.

See GBLACKMANHARRIS to generate a 4 term Blackman-Harris window.

Blackman, Blackman-Harris, Flattop, Hamming, Hanning and Kaiser Windows are useful in creating FIR filters and in preprocessing series for FFT calculations.

GBLACKMAN can also be invoked as GBLCKMAN.