Methods for recovering the input signals of nonlinear nonstationary dynamic systems
摘要
The article considers the problem of recovering input electrical, radio, optical, and vibroacoustic signals, which is relevant for modern metrology and measurement technology. Recovery of input signals in measurement systems is required for a wide range of tasks in various fields of science and technology. In general, the models of linear dynamic systems are considered for the recovery of input signals. However, due to changes in the operating conditions of dynamic systems, where the nonstationarity and nonlinearity of processes become more pronounced, a need arises for methods that can provide a means to recover input signals while taking into account their nonlinearity and nonstationarity. The article proposes methods for recovering the input signals of nonlinear nonstationary dynamic (continuous and discrete) systems described by the Volterra functional series. These methods are based on solving a nonlinear integral equation based on a truncated Volterra series. Input signal recovery is carried out under the assumption that integral transforms of Volterra kernels have factorization based on Borel’s theorem, which yields a nonlinear algebraic equation. The article also proposes methods for recovering the input signals of continuous nonlinear dynamic systems described by a truncated Volterra series and its discrete analogs. For the recovery of input signals in continuous systems, the integral Laplace transform is used, while for discrete systems, the Z-transform is applied. An example is given of a mathematical solution to the problem of recovering a discrete one-dimensional signal, illustrating the validity and effectiveness of the developed methods. The results of studies on signal recovery in nonlinear dynamic systems can be used by experts involved in theoretical research and mathematical modeling in the field of digital signal processing and vector analysis of electrical circuits.