A Theoretical Investigation of a Method for Analyzing Random Signals.

摘要

Progress was made along several directions including one new approach. The sequence of development through the summer progressed roughly as follows. Work was begun on developing tables of probabilities based on earlier results. In the process of implementing the formulas however, certain conceptual difficulties arose. While the formulas are correct, Rice's representation proved cumbersome in this application. In the process of solving this problem another approach to the probability of a backward crossing was discovered and, after a period of theoretical work, was found to produce a formulas which is simple and in closed form. The derivation however involved an assumption which appears to be sound but has not yet been completely justified theoretically. With limited time it was felt a simulation would prove valuable as an empirical verification of the results obtained. A study was made into ways of simulating on a digital computer the continuous zero crossing and counting properties of the patented device. Algorithms were developed and programs wwitten, tested, and debugged. A successful simulation was run for white noise as well as certain deterministic signals. (Author)