Signal conversion systems

Signals, in any form of material representation, contain certain useful information. If during signal transformations there is a violation of the information contained in them (partial loss, quantitative change in the ratio of information components or parameters, etc.), then such changes are called signal distortions . If the useful information remains unchanged or adequate to the content in the input signal, then such changes are called signal transformations .

Any changes in signals are accompanied by a change in their spectrum, and by the nature of this change they are divided into two types: linear and nonlinear. By nonlinear include changes in which a part of the signal spectrum, new harmonic components that are not in the input signal. With linear changes in the signals, the amplitudes and / or the initial phases of the harmonic components of the spectrum change. Both linear and nonlinear changes in signals can occur both with the preservation of useful information and with its distortion. It depends not only on the nature of the change in the signal spectrum, but also on the spectral composition of the most useful information.

General concept of systems. Signal conversion and processing is carried out in systems. The concepts of a signal and a system are inseparable, since any signal exists within a system. The signal processing system can be implemented both in material form (a special device, a measuring device, a set of physical objects with a certain structure of interaction, etc.), and programmatically on a computer or any other specialized computing device. The form of the implementation of the system is not essential, and only determines its capabilities in the analysis and processing of signals.

Regardless of the purpose, the system always has an input to which an external input signal is applied, in general multidimensional, and an output from which the processed output signal is taken. The system itself is a system operator (algorithm) for converting the input signal s (t) - action or excitation , into a signal at the output of the system y (t) - the response or output reaction of the system. Symbolic designation of the transformation operation (signal transformation): y (t) = T [s (t)].

The system operator T is a set of transformation rules for the signal s (t) into the signal y (t). So, for example, in the simplest case, such a rule can be a conversion table for input signals into outputs.

For deterministic input signals, the relationship between output and input signals is always uniquely determined by the system operator. If a random input process is implemented at the input of the system, the statistical characteristics of the signal (mathematical expectation, variance, correlation function, etc.) change, which is also determined by the system operator.

For a complete definition of the system, it is necessary to specify the nature, type and range of permissible values ​​of input and output signals. According to the type of input signal processing, they are usually subdivided into continuous-time systems for processing signals during measurements, and digital systems for processing data recorded on intermediate media. The totality of the system operator T and the areas of input and output signals forms a mathematical model of the system.

Linear and non-linear systems comprise two main classes of signal processing systems.

The term linearity means that the signal conversion system must have an arbitrary, but necessarily linear relationship between the input signal (excitation) and the output signal (response) with a certain change in the spectral composition of the input signal (amplification or suppression of certain frequency components of the signal. In nonlinear systems, the connection between the input and output signal is determined by an arbitrary nonlinear law with the addition of the frequency content of the input signal with frequency components that are absent in the input signal.

Stationary and non-stationary systems. A system is considered stationary and hasconstant parametersif its properties (the mathematical algorithm of the transformation operator), within a given accuracy, do not depend on the input and output signals and do not change either in time or on any other external factors. Otherwise, the system is nonstationary, and is calledparametricor asystem with variable parameters... Among the latter, so-called adaptive data processing systems are of great importance. In these systems, for example, estimation of certain parameters of input and output signals is carried out, based on the comparison of which, the conversion parameters (transient response of the system) are adjusted in such a way as to provide optimal signal processing conditions in terms of performance or to minimize the processing error.

Basic system operations. The basic linear operations, from which any linear transformation operators can be formed, include operations of scalar multiplication, shift, and addition of signals:

y (t) = c ґ s (t), y (t) = s (t- D t), y (t) = a (t) + b (t).

For nonlinear systems, we single out an important type of inertia-free operations of nonlinear signal transformation, the results of which depend only on its input values. These include, for example, the operations of squaring and logarithm of the signal:

y (t) = [s (t)] ² , y (t) = log [s (t)].