DADiSP Worksheet Functions > Function Categories > Fourier Transforms and Signal Processing > HANNING
Multiplies a series with a Hanning window.
HANNING(series, ampflag, "sym")
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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"sym" |
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Optional. A string, the symmetry flag:
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HANNING(N, ampflag, "sym")
N |
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An integer, the window length. |
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ampflag |
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Optional. An integer, the amplitude correction flag:
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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(hanning(W1))
W3: spectrum(hanning(W1, 1))
The MAX of W2 == 0.5005 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 symmetric Hanning window. The symmetric window follows the form:
where n is the nth point (1 <= n <= N) and N = L+1 where L is the number of points to generate. The leading zero is removed.
W4: hanning(1000, "periodic")
Creates a 1000 point periodic Hanning window that conforms to the ISO 18431-1 standard.
where n is the nth point (1 <= n <= N) and N = L where L is the number of points to generate. The leading zero is preserved.
W1: hanning(1000, "direct")
Creates a 1000 point direct Hanning window by the formula:
where n is the nth point (1 <= n <= N) and N is the number of points to generate. The leading and trailing zeros are preserved.
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 = hanning(s) * rms(s) / rms(hanning(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 "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 leading zero is removed.
"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 direct form of the window can be constructed by setting N to
For the default Hanning window:
See GHANNING to generate a Hanning window.
The Hanning window is sometimes referred to as a Hann window.