Impact of colored noise in pulse amplitude measurements: A time-domain approach using differintegrals

In particle detectors, pulse shaping is the process of changing the waveform of the pulses in order to maximize the signal to noise ratio. This shaping usually only takes into account white, pink (flicker) and red (Brownian) noise. In this paper, a generalization of noise indexes as a function to an arbitrary fβfβ noise type, where β is a real number, is presented. This generalization has been created using the differintegral operator, defined in Fractional Calculus. These formulas are used to calculate the Equivalent Noise Change (ENC) in detector particle systems.