Quadratic System Identification: a statistical framework for the paired-pulse paradigm

System Identification refers to the problem of identifying a model or description of a system based on a stretch of input and the corresponding output from the system. The paired-pulse paradigm or the conditioning test pulse paradigm is often used in neurophysiology experiments. In this work we provide a statistical framework for the conditioning test pulse paradigm which also serves as a system identification tool for quadratic or second order Volterra systems. A nonparametric spectral domain based methodology is proposed for the quadratic system identification. It is shown that by carrying out the analysis in the spectral domain one needs to perform only a single set of double pulse experiments as opposed to multiple sets of experiments in the time domain. Simulation studies are performed to assess the performance of the methodology and to study the conditions under which the methods are expected to perform well.