Models of Measuring Signals and Fields

Abstract

The methodological aspects of the analysis of multidimensional signals and fields are highlighted. Mathematical models of measuring signals and fields are systematized, the main spatio-temporal models of quasi-determined signals are considered—continuous and discrete, complex-valued, periodic. Some facts of the theory of orthogonal signals and orthogonal bases are considered, the possibilities of their use for measurements are analyzed. Signal models that are described by random processes are considered. The definitions of a random process stationary in the broad and narrow sense of random processes, a linear random process, a harmonized random process, a periodically correlated random process are given. Models of multidimensional signals and spatio-temporal random fields are considered. Characteristics of signals and spatio-temporal random fields are given taking into account their structure for research by means of measuring equipment. It is concluded that the creation of hardware and information support for measurements and monitoring requires the coordination of physical and probabilistic measures to assess the characteristics of multidimensional signals and fields in accordance with the requirements of the concept of measurement uncertainty.