Computing the Optimal Filtering Coefficients (OFC's)

where A is the amplitude of the predicted physics signal, g(t) is the normalized shape of the input signal, g'(t) is its first derivative and n(t) is the noise component given by the noise autocorrelation matrix.

• The normalized shape of the physics signal is given by:

and the meaning of parameters τcali, fstep, τ0, τr, Td and τdiff is explained here.

• A and ADCpeak in Fig. 3 are equivalent.  A (or  ADCpeak) and it's location in time, τ, can be computed using a weighted sum:

A = Σi ai si
Aτ= Σi bi si,

where ai and bi are energy and time Optimal Filtering Coefficients (OFC's), and Σi is over the ADC samples si where pedestal has been subtracted.