GFLATTOP

Purpose:

Generates a Flattop Window.

Syntax:

GFLATTOP(N, spacing, type, "sym")

N

-

An integer, the number of points to generate.

spacing

-

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

type

-

Optional. An integer, the generation method.

0:

ISO 18431-1 4 point method (default)

1:

2 point formula

2:

Alternate 4 point formula

3:

HP P301

4:

HP 4 point formula

5:

Modified HP P401 5 point formula

6:

Rohde & Schwartz 4 point formula

"sym"

-

Optional. A string, the symmetry flag.

"symmetric"

:

Starting and ending points are equal.

"periodic"

:

Periodically extended window where the trailing symmetric point is removed. Conforms to the ISO standard (default).

"iso"

:

Same as "periodic".

Returns:

A series.

Example:

gflattop(100, .01)

 

generates a periodic 100-point Flattop Window using the following 4 point 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.

Remarks:

 

The Flattop window preserves the amplitude of a series at the expense of frequency resolution. It will accurately measure the amplitude of a series at any frequency, even if the frequency lies between FFT bins.

 

The periodic flattop window is constructed by the formula of the form:

 

 

where N is the length of the window and n is the nth point (1 <= n <= N).

 

The symmetric flattop window is constructed by the formula of the form:

 

 

where N is the length of the window and n is the nth point (1 <= n <= N).

 

The type parameter specifies the values of the flattop window coefficients. The following types are supported:

 

For type 0, ISO 18431-1 (default):

 

 

 

For type 1, two point flattop window:

 

 

 

For type 2, alternate four point flattop window:

 

 

 

For type 3, three point HP P301 flattop window:

 

 

 

For type 4, HP four point window:

 

 

 

For type 5, modified HP P401 five point window:

 

 

 

For type 6, Rohde & Schwartz four point 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 first point.

 

"Periodic" or "iso" creates a periodic window function useful in spectrum analysis applications where the starting zero is preserved and the trailing zero is removed. "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.

 

Because the ISO 18431-1 standard specifies a periodic flattop window, GFLATTOP uses "periodic" as the default for the "sym" flag.

 

Use FLATTOP to automatically create and multiply a Flattop window with a series. For example:

 

flattop(W1)

 

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

 

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

See Also:

FFT

FLATTOP

GBLACKMAN

GBLACKMANHARRIS

GFLATTOPWIN

GHAMMING

GHANNING

GKAISER

PSD

SPECTRUM