# GHAMMING

## Purpose:

Generates a Hamming Window.

## Syntax:

GHAMMING(N, spacing, alpha, "sym")

N

-

An integer, the number of points to generate.

spacing

-

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

alpha

-

Optional. A real, the scaling parameter. Defaults to 0.54.

"sym"

-

Optional. A string, the symmetry flag.

 "symmetric" : Starting and ending points are equal, but leading and trailing zeros are removed (default). "periodic" : Periodically extended window where the leading zero is preserved. Conforms to the ISO standard. "iso" : Same as "periodic".

A series.

## Example:

ghamming(100,.01)

generates a 100-point symmetric Hamming window using the following formula: where α is the default value 0.54, 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:

ghamming(100,.01, "periodic")

generates a 100-point periodic Hamming window using the following formula: where α is the default value 0.54, 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.

## Remarks:

A Hamming Window with α = 0.5 is identical to a HANNING Window.

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 default Hamming window: Use HAMMING to automatically create and multiply a Hamming window with a series. For example:

hamming(W1)

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

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

FFT

FLATTOP

GBLACKMAN

GBLACKMANHARRIS

GCHEBWIN

GHANNING

GKAISER

GTAYLORWIN

HAMMING

PSD

SPECTRUM

## References:

Oppenheim and Schafer.

Digital Signal Processing

Prentice Hall, 1975

Digital Signal Processing Committee

Programs for Digital Signal Processing

I.E.E.E. Press, 1979