System Identification with Threshold Measurements

A method has been developed to analyze systems which have threshold properties. The only information about the system response that is used in the analysis is whether or not this response exceeds a fixed threshold of unknown magnitude. There are many biological systems that fall into this category of systems, for example, the auditory system, the visual system, electrical stimulation of nerve cells, etc. However, any network to which an arbitrary amplitude has been assigned and which the response has to exceed as an artificial threshold could be analyzed with the methods outlined in this paper. The cases of a simple linear system and first- and second-order photochemical reactions are discussed extensively. It is shown that due to the limited output information available, often no unique system characterization is possible. However, the method can be a powerful aid in the selection between various alternatives. The influence of possible nonlinear operators in the system has been analyzed, and the result turns out to be very dependent upon the location and character of these operators. Some classic vision-research experiments are discussed as examples to illustrate the application of the analysis put forward in this paper.