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This is a delicate procedure, in practice, as the division is sensitive to the small high-frequency errors. Direct application of this results in very noisy results. A good remedy is a low-pass filter on the spectrum of the measured signal (taking care to preserve the shape of the signal by keeping the cutoff well above the highest relevant frequencies).
This is a delicate procedure, in practice, as the division is sensitive to the small high-frequency errors. Direct application of this results in very noisy results. A good remedy is a low-pass filter on the spectrum of the measured signal (taking care to preserve the shape of the signal by keeping the cutoff well above the highest relevant frequencies).
== Modeling the HPD spectrum ==
[[Image:HPDspectra.png|thumb|300px]]
The HPD spectra collected from large pulses should essentially be a convolution of the Poisson distribution, in the limit of high mean count, with the electronic noise function, which is known to be broad enough to make individual photon peaks impossible to resolve. Both of these functions are Gaussian and the result should be a Gaussian as well. The measured spectra show a peculiar deviation (shown on the right.)