Multiplies a series with a Hanning window.
HANNING(series, ampflag, "sym")
series 
 
A series or array. 

ampflag 
 
Optional. An integer, the amplitude correction flag:


"sym" 
 
Optional. A string, the symmetry flag:

HANNING(N, ampflag, "sym")
N 
 
An integer, the window length. 

ampflag 
 
Optional. An integer, the amplitude correction flag:


"sym" 
 
Optional. A string, the symmetry flag:

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 n^{th} 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 184311 standard.
where n is the n^{th} 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 n^{th} 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 184311 standard for windowing functions.
The Hamming, Hanning, Flattop and Blackman windows are part of the family of cosine window functions. The ISO 184311 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.