# KAISER

## Purpose:

Multiplies a series with a Kaiser window.

## Syntax:

KAISER(series, ampflag, beta)

series

-

A series or array.

ampflag

-

Optional. An integer, the amplitude correction flag:

 0 : do not correct amplitude (default) 1 : correct amplitude 2 : correct RMS amplitude 3 : correct mean squared amplitude

beta

-

Optional. A real, the scaling factor. Defaults to 7.865.

## Alternate Syntax:

KAISER(N, ampflag, beta)

N

-

An integer, the window length.

ampflag

-

Optional. An integer, the amplitude correction flag:

 0 : do not correct amplitude (default) 1 : correct amplitude 2 : correct RMS amplitude 3 : correct mean squared amplitude

beta

-

Optional. A real, the scaling factor. Defaults to 7.865.

## Returns:

A series or array.

## Example:

W1: gsin(1000, .001, 45)

W2: spectrum(kaiser(W1))

W3: spectrum(kaiser(W1, 1))

The MAX of W2 == 0.4389 and the MAX of W3 == 1.0. The amplitude of the spectrum in W3 has been corrected to take into account amplitude effects of the Kaiser window.

## Remarks:

If ampflag == 1, the correction factor is the mean of the spectral window. This assures that the spectrum of a sinusoid of amplitude A has a peak of A.

If ampflag == 2, the correction is applied as follows:

w = kaiser(s) * rms(s) / rms(kaiser(s))

This assures that:

sqrt(area(psd(w))) == rms(s) approximately

If ampflag == 3, the correction is applied as follows:

w = winfun(s) / sqrt(mean(win * win)

where win is the windowing function.

The Kaiser window is generated using the following formula: where n is the nth point (1 <= n <= N), Io is the modified zeroth order Bessel function of the first kind. Default β is 7.865 and N is the number of points to generate.

See GKAISER to generate a Kaiser window.

BESSELI

BLACKMAN

FLATTOP

GKAISER

HAMMING

HANNING

PSD

SPECTRUM

WINFUNC