Multiplies a series with a Flattop window.
FLATTOP(series, ampflag, type, "sym")
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series |
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A series or array. |
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ampflag |
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Optional. An integer, the amplitude correction flag:
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type |
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Optional. An integer, the window generation method:
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"sym" |
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Optional. A string, the symmetry flag:
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FLATTOP(N, ampflag, type, "sym")
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N |
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An integer, the length of the window. |
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ampflag |
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Optional. An integer, the amplitude correction flag:
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type |
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Optional. An integer, the window generation method:
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"sym" |
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Optional. A string, the symmetry flag:
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A series or array.
W1: gsin(1000, .001, 45)
W2: spectrum(flattop(W1))
The MAX of W2 == 1.0 at 45 Hertz.
W3: flattop(1000, "symmetric")
Generates a 1000 point symmetric flattop window.
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.
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 = flattop(s) * rms(s) / rms(flattop(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 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, FLATTOP uses "periodic" as the default for the "sym" flag.
See GFLATTOP to generate a Flattop window.
See FLATTOPWIN for an implementation of the alternative 4 term flattop window (type == 2).