Signal and linear systems theory

In the 18th century, the concept of a function entered into the theory of mathematics as a certain dependence of any quantity y on another quantity - the independent variable x , with a mathematical record of such a dependence in the form y (x) . Pretty soon the mathematics of functions became the basic foundation of the theory of all natural and technical sciences. Functional mathematics acquired particular importance in communication technology, where time functions of the form s (t), v (f), etc., used to transmit information, began to be called signals.

In technical branches of knowledge, the term "signal" (signal, from the Latin signum - sign) is very often used in a wide semantic range, without adhering to strict terminology. It is also understood as a technical medium for the transmission, treatment and use of information - electrical, magnetic, optical signal; and a physical process, which is a material embodiment of an information message - a change in any parameter of an information carrier (voltage, frequency, power of electromagnetic oscillations, intensity of a luminous flux, etc.) in time, in space or depending on the change in the values ​​of any other arguments (independent variables); and the semantic content of a particular physical state or process, such as traffic signals, audible warning signals, and the like.All these concepts are united by the final purpose of signals. This is certain information, messages, information about any processes, states or physical quantities of objects of the material world, expressed in a form that is convenient for the transmission, processing, storage and use of this information.

The term "signal" is very often equated with the concepts "data" and "information" . Indeed, these concepts are interrelated and do not exist one without the other, but belong to different categories.

The concept of information has many definitions, from the broadest (information is a formalized reflection of the real world) to practical (information and data that are the object of storage, transmission, transformation, perception and management). At present, world science is more and more inclined to the point of view that information, along with matter and energy, belongs to the fundamental philosophical categories of natural science and belongs to one of the properties of the objective world, albeit somewhat specific. As for "data" (from the Latin datum - fact), it is a set of facts, results of observations, measurements about any objects, phenomena or processes in the material world, presented in a formalized form, quantitative or qualitative. This is not informationbut only the attribute of information is a raw material for obtaining information through appropriate processing and interpretation (interpretation).

Science and technology are international, and use mostly commonly accepted terms, most of which are in English. The term "signal" in world practice is generally accepted to characterize the form of data presentation, in which data is considered as a result of some measurements of the object of research in the form of a sequence of scalar values ​​(analog, numerical, graphic, etc.) depending on the change in any variable values (time, energy, temperature, spatial coordinates, etc.). Taking this into account, in what follows, the term "signal" in the narrow sense of this word will mean in some way an ordered mappingin a change in the physical state of an object - a material carrier of a signal, certain data on the nature of changes in space, in time or in any other variable of physical quantities, physical properties or physical state of the object of research. And since the data contain information both about the main target parameters of the object of research, and about various accompanying and interfering measurement factors, in the broad sense of this word, it can be considered that the signal is a carrier of general measurement information. In this case, the material form of signal carriers (mechanical, electrical, magnetic, acoustic, optical, and any other), as well as the form of display in any physical parameters or processes of the carriers, does not matter . An informative signal parameter can be any parameter of the signal carrier, functionally related to the values ​​of the information data.

A signal, in the most general sense, is the dependence of one quantity on another, and from a mathematical point of view it is a function. The most common representation of signals is in electrical form in the form of voltage versus time U (t). So, for example, the signal of the change in the magnetic field strength along the aerial survey profile is both the time sequence of the change in the electric voltage at the output of the aeromagnetometer sensor, and the recording of this voltage on the recorder tape, and the sequential values ​​of digital readings during the processing of the recorder tapes and inputting the signal into the computer.