A system for detecting a neuronal action potential signal from electrically stimulated neural tissue, the system comprising: a physiological database containing physiological data characterizing neural tissue response to electrical stimulation, wherein the physiological data is characterized by a plurality of Gaussian mixture models (GMMs) for known NAP signals; and a response measurement module configured to: i. obtain a compound discharge latency distribution (CDLD) P of the neural tissue defining how many nerve fibers discharge as a function of post-stimulus time by solving for P the inverse problem of the convolution R = N ∫ − ∞ t P τ U t − τ dτ, optionally by using a fast-Fourier-transform algorithm for the deconvolution, wherein: (a) R is a tissue response measurement signal taken responsive to electrical stimulation of the neural tissue by a stimulation electrode and comprising the NAP signal, artifacts due to stimulation and other sources, and noise, and (b) U is a known elementary unit response signal representing voltage change at a measurement electrode due to an activation of a single nerve fiber due to the electrical stimulation, and wherein N represents the number of excited nerve fibers observable at the measurement electrode; ii. compare the CDLD to physiological data from the physiological database by fitting to the CDLD parameters of the GMMs to detect the NAP signal from the tissue response measurement signal. a physiological database containing physiological data characterizing neural tissue response to electrical stimulation, wherein the physiological data is characterized by a plurality of Gaussian mixture models (GMMs) for known NAP signals; and a response measurement module configured to: i. obtain a compound discharge latency distribution (CDLD) P of the neural tissue defining how many nerve fibers discharge as a function of post-stimulus time by solving for P the inverse problem of the convolution R = N ∫ − ∞ t P τ U t − τ dτ, optionally by using a fast-Fourier-transform algorithm for the deconvolution, wherein: (a) R is a tissue response measurement signal taken responsive to electrical stimulation of the neural tissue by a stimulation electrode and comprising the NAP signal, artifacts due to stimulation and other sources, and noise, and (b) U is a known elementary unit response signal representing voltage change at a measurement electrode due to an activation of a single nerve fiber due to the electrical stimulation, and wherein N represents the number of excited nerve fibers observable at the measurement electrode; ii. compare the CDLD to physiological data from the physiological database by fitting to the CDLD parameters of the GMMs to detect the NAP signal from the tissue response measurement signal. i. obtain a compound discharge latency distribution (CDLD) P of the neural tissue defining how many nerve fibers discharge as a function of post-stimulus time by solving for P the inverse problem of the convolution R = N ∫ − ∞ t P τ U t − τ dτ, optionally by using a fast-Fourier-transform algorithm for the deconvolution, wherein: (a) R is a tissue response measurement signal taken responsive to electrical stimulation of the neural tissue by a stimulation electrode and comprising the NAP signal, artifacts due to stimulation and other sources, and noise, and (b) U is a known elementary unit response signal representing voltage change at a measurement electrode due to an activation of a single nerve fiber due to the electrical stimulation, and wherein N represents the number of excited nerve fibers observable at the measurement electrode; (a) R is a tissue response measurement signal taken responsive to electrical stimulation of the neural tissue by a stimulation electrode and comprising the NAP signal, artifacts due to stimulation and other sources, and noise, and (b) U is a known elementary unit response signal representing voltage change at a measurement electrode due to an activation of a single nerve fiber due to the electrical stimulation, and wherein N represents the number of excited nerve fibers observable at the measurement electrode; ii. compare the CDLD to physiological data from the physiological database by fitting to the CDLD parameters of the GMMs to detect the NAP signal from the tissue response measurement signal.