Presentation and Analysis of Continuous Signals in the Space of Complex Exponential Models

Abstract

For approximation and time-frequency analysis of continuous signals, it is proposed to use non-causal complex exponential models defined in the general case on an infinite two-way time interval. It is shown that the space of such model signals is Euclidean and rigorous analytical expressions are obtained for their main characteristics in the time domain and spectral domain - convolutions of signals, cross-correlation functions, spectrum and cross-spectral densities, etc. The possibilities of applying the obtained formulas in the Matlab system are demonstrated.