Обнаружение сигналов с использованием ортогонального базиса функций Гаусса - Эрмита

Abstract

The analysis of the shape and parameters of signals is a key part of the signal processing. As a rule in practicable task, the shape of the input signal is known and identification of the unknown parameters (amplitude, duration, location or time of arrival, etc.) is required, then the dynamics of the signal sequence in the process under study is important as well. Thus, the problem is the most reliable detection of the desired signal on the background of random noise and the most accurate measurement of its parameters. It is known that a solution of such problems concerns optimal filtering. The main abstract of the method of the signal detection, based on orthogonal basis functions of the Gauss-Hermite functions, is described. The method is founded on the matched filtering principles, it allows tracking not only the dynamics of the signal under investigation, but also its local features, which provide additional diagnostic information. The verification method is carried out on a real signal of a phase measuring complex. The signal represents a sequence of pulses as a mixture component of the respiratory and cardiac activity of a medical patient.