PSD

Tentative PSD Algorithm

I have gotten caught up in doing PSD (Pulse Spectrum Discrimination) on our films.  Results seem promising!

I worked a little more on the mathematics of the Falling Balls / Gaussian Distribution.  The idea is to integrate all of the probabilities across the rows
$$ Ae^{-(x-\mu)^2/2\sigma^2} ?=\int_{0}^{n-1} \frac{r!}{n!(r-n!)}p^{n-1} $$
- I think that will provide the probability density function (PDF). Turns out the continuous analog of the factorial  is the gamma function, (for positive values, which we have).    Turns out that nobody has ever analytically integrated the gamma function before, either.  So now I am looking for a nice, integratable approximation for the factorial / gamma function (trying to do a Taylor series expansion of the terms I get from the Sterling Approximation).