/*
The gaussian(x) = (exp(-48*((i-(n+1)/2)/(n+1))^2)-exp(-12))/(1-exp(-12));
For power we need thearea under the square of this window:
Integrate (gaussian(i)^2,i=1..n) =
(sqrt(Pi)*sqrt(3)*sqrt(2)*erf(2*(n-1)*sqrt(3)*sqrt(2)/(n+1))*(n+1)+
24*exp(-24)*(n-1)+
-4*sqrt(Pi)*sqrt(3)*exp(-12)*erf(2*(n-1)*sqrt(3)/(n+1))*(n+1))/
(24 * (-1+exp(-12))^2)
To compare with the rectangular window we need to divide this by the
window width (n-1) x 1^2.
*/
static double gaussian_window_squared_correction (long n) {
double e12 = exp (-12), denum = (e12 - 1) * (e12 - 1) * 24 * (n - 1);
double sqrt3 = sqrt (3), sqrt2 = sqrt (2), sqrtpi = sqrt (NUMpi);
double arg1 = 2 * sqrt3 * (n - 1) / (n + 1), arg2 = arg1 * sqrt2;
double p2 = sqrtpi * sqrt3 * sqrt2 * (1 - NUMerfcc (arg2)) * (n + 1);
double p1 = 4 * sqrtpi * sqrt3 * e12 * (1 - NUMerfcc (arg1)) * (n + 1);
return (p2 - p1 + 24 * (n - 1) * e12 * e12) / denum;
}
/*
The gaussian(x) = (exp(-48*((i-(n+1)/2)/(n+1))^2)-exp(-12))/(1-exp(-12));
For power we need the area under the square of this window:
Integrate (gaussian(i)^2,i=1..n) =
(sqrt(Pi)*sqrt(3)*sqrt(2)*erf(2*(n-1)*sqrt(3)*sqrt(2)/(n+1))*(n+1) + 24*exp(-24)*(n-1)+
-4*sqrt(Pi)*sqrt(3)*exp(-12)*erf(2*(n-1)*sqrt(3)/(n+1))*(n+1))/ (24 * (-1+exp(-12))^2),
where erf(x) = 1 - erfc(x) and n is the windowLength in samples.
To compare with the rectangular window we need to divide this by the window width (n -1) x 1^2.
*/
static void _Spectrogram_windowCorrection (Spectrogram me, long numberOfSamples_window) {
double windowFactor = 1;
if (numberOfSamples_window > 1) {
double e12 = exp (-12);
double denum = (e12 - 1) * (e12 - 1) * 24 * (numberOfSamples_window - 1);
double arg1 = 2 * NUMsqrt3 * (numberOfSamples_window - 1) / (numberOfSamples_window + 1);
double arg2 = arg1 * NUMsqrt2;
double p2 = NUMsqrtpi * NUMsqrt3 * NUMsqrt2 * (1 - NUMerfcc (arg2)) * (numberOfSamples_window + 1);
double p1 = 4 * NUMsqrtpi * NUMsqrt3 * e12 * (1 - NUMerfcc (arg1)) * (numberOfSamples_window + 1);
windowFactor = (p2 - p1 + 24 * (numberOfSamples_window - 1) * e12 * e12) / denum;
}
for (long i = 1; i <= my ny; i++) {
for (long j = 1; j <= my nx; j++) {
my z[i][j] /= windowFactor;
}
}
}
