Thus, a signal is a physical process whose parameters contain information (message) and which is suitable for processing and transmission over a distance.

One-dimensional and multidimensional signals. A typical signal for radio engineering is the voltage at the terminals of a circuit or the current in a branch. Such a signal, described by a single function of time, is usually called one-dimensional.

However, sometimes it is convenient to introduce multidimensional, or vector, signals of the form

formed by some set of one-dimensional signals. The integer N is called the dimension of such a signal.

Note that a multidimensional signal is an ordered collection of one-dimensional signals. Therefore, in the general case, signals with different orders of components are not equal to each other.

Analog, discrete and digital signals. Concluding a brief overview of the principles of classification of radio signals, we note the following. Often the physical process that generates a signal develops over time in such a way that the signal values ​​can be measured at any time. Signals of this class are usually called analog (continuous). The term “analog signal” emphasizes that such a signal is “analogous”, completely similar to the physical process generating it.

A one-dimensional analog signal is clearly represented by its graph (oscillogram), which can be either continuous or with break points.

.

Multidimensional signal models are especially useful in cases where the functioning of complex systems is analyzed using a computer.

Deterministic and random signals. Another principle of classification of radio signals is based on the possibility or impossibility of accurately predicting their instantaneous values ​​at any time.

If the mathematical model of the signal allows such a prediction to be made, then the signal is called deterministic. The methods for specifying it can be varied - a mathematical formula, a computational algorithm, and finally, a verbal description.

Analogue (continuous), discrete and digital signals. Often the physical process that generates a signal develops over time in such a way that the signal values ​​can be measured at any time. Signals of this class are usually called analog (continuous). The term “analog signal” emphasizes that such a signal is “analogous”, completely similar to the physical process generating it.

A one-dimensional analog signal is clearly represented by its graph (oscillogram), which can be either continuous or with break points.

Initially, radio engineering used exclusively analog signals. Such signals made it possible to successfully solve relatively simple technical problems (radio communications, television, etc.). Analogue signals were easy to generate, receive and process using the means available at that time.

Increased demands on radio systems and a variety of applications have forced us to look for new principles for their construction. In some cases, analog ones have been replaced by pulsed systems, the operation of which is based on the use of discrete signals. The simplest mathematical model of a discrete signal is a countable set of points ( - an integer) on the time axis, in each of which the reference value of the signal is determined. Typically, the sampling step for each signal is constant.

One of the advantages of discrete signals over analog signals is that there is no need to reproduce the signal continuously at all times. Due to this, it becomes possible to transmit messages from different sources over the same radio link, organizing multi-channel communication with time-separated channels.

Intuitively, fast time-varying analog signals require a small step size to be sampled.

A special type of discrete signals are digital signals. They are characterized by the fact that the reference values ​​are presented in the form of numbers. For reasons of technical convenience of implementation and processing, binary numbers with a limited and, as a rule, not too large number of digits are usually used. Recently, there has been a trend towards widespread implementation of systems with digital signals. This is due to the significant advances achieved by microelectronics and integrated circuit technology.

It should be borne in mind that in essence any discrete or digital signal (we are talking about a signal - a physical process, and not about a mathematical model) is an analog signal.

Strictly speaking, deterministic signals, as well as deterministic processes corresponding to them, do not exist. The inevitable interaction of the system with the physical objects surrounding it, the presence of chaotic thermal fluctuations and simply incomplete knowledge about the initial state of the system - all this forces us to consider real signals as random functions of time.

In radio engineering, random signals often manifest themselves as interference, preventing the extraction of information from a received oscillation. The problem of combating interference and increasing the noise immunity of radio reception is one of the central problems of radio engineering.

The concept of a "random signal" may seem contradictory. However, this is not true. For example, the signal at the output of a radio telescope receiver aimed at a source of cosmic radiation represents chaotic oscillations, which, however, carry a variety of information about a natural object.

There is no insurmountable boundary between deterministic and random signals. Very often, in conditions where the level of interference is significantly less than the level of a useful signal with a known shape, a simpler deterministic model turns out to be quite adequate to the task.

Signal modeling begins, first of all, with their classification. There are several classification methods, one of which is shown in Fig. 1.6.

Rice. 1.6.

It should be borne in mind that electrical signals operate in radio circuits.

Electrical signals are time-varying electrical currents or voltages.

All electrical signals are divided into deterministic And random.

Deterministic signals are described by a given time function, the value of which at any time is known or can be predicted with probability one.

Deterministic signals include so-called test or test signals. They are widely used in various studies, when testing radio equipment, in radio measurement practice, etc.

To describe random signals, a probabilistic approach is used, in which random signals are considered as random processes.

Random signal - this is a random process that changes in a given dynamic range and takes on any value from the range with a probability of less than one.

As a rule, random signals are chaotic functions of time, and the choice of its mathematical model depends on the law of its distribution (uniform, normal or Gaussian, Poisson, etc.).

All random signals are divided into stationary, non-stationary and ergodic.

A random process is called stationary if its statistical characteristics (at least the mathematical expectation m and variance a2) do not depend on time. Otherwise the process is not stationary.

A process is called ergodic if its average over the ensemble of implementations is equal to the time average.

All ergodic processes are stationary, but not all stationary processes are ergodic.

Most random signals in radio engineering systems are ergodic, therefore, to describe a mathematical model, it is enough to average a random signal over an ensemble of implementations or over time.

Real signals are always random to some extent. Firstly, the signal is always distorted in the transmitter and receiver circuits due to the random nature of changes in the parameters of their elements. Secondly, in the transmission medium, the signal is always affected by random interference, turning it into a random signal at the receiver input. At the same time, in many cases, a real signal with a certain degree of accuracy can be considered as deterministic, which facilitates their analysis.

All signals (deterministic and random) are divided into periodic and non-periodic.

Periodic signals are characterized by the property of repeatability after a certain period of time T, called a period: s(t) = s(t + nT),n= 1,2,3,.... (1.2)

Here s(t) is the signal under consideration; T is the period of its repetition; f = 1/T - signal repetition frequency.

If during transmission T changes in an arbitrary manner, then the signal is called non-periodic. If the period T is repeated after a sufficiently large period of time, then the signal is called quasiperiodic or pseudorandom.

Signals, even analogue ones, that exist only in one time interval are classified as pulsed. Figure 1.7 shows some types of the signals listed above.

Rice. 1.7, a describes, for example, a deterministic discrete signal with a repetition period of rectangular pulses T and pulse duration T s in a ratio of 2: 1 (meander). The ratio Q = T/T c is called the duty cycle of the signal. For the signal Fig. 1.7, and it is equal to 2, and for the signal in Fig. 1.7,c - 3. Figure 1.7,c shows a periodic signal with Q = 3. Figures 1.7, b and d illustrate random and non-periodic signals, respectively. If we select only one pulse in all the figures, we obtain, accordingly, a pulse signal.

Rice. 1.7.

When considering various signals, they usually resort to four types of their representation:

• - temporary;
• - spectral;
• - correlation;
• - vector.

Temporary performance.

The temporal representation is based on viewing the signal as a function of time. Depending on the position of the signal relative to the observer, its time function will, generally speaking, be different. This can be explained quite simply using the diagram shown in Fig. 1.8.

Rice. 1.8.

Let us assume that the “observer” is at a point characterized by the observation interval t4 - ts. It is obvious that at time tj only a certain point is observed, reflecting the fact of the presence of a signal, and nothing can be said about its structure. As it approaches the “observer,” the signal begins to stretch in time and we see some kind of its structure (time interval t2 - In this interval, the structure of the signal corresponds to its true structure, but the pulse repetition rate will not correspond to the actual one. It will become such only in interval t 4 - t 5, when the location of the signal corresponds to the position of the “observer”. In this interval, we will be able to measure the true parameters of the signal - its amplitude, frequency and phase.

The Doppler effect is based on this property, which is easy to observe in practice when a car with a siren on drives past the observer. Suppose the siren produces a certain tone, and it does not change. When the car is not moving relative to the observer, then he hears exactly the tone that the siren makes. But if the car moves closer to the observer, the frequency of the sound waves will increase, and the observer will hear a higher pitch than the siren actually emits. At the moment when the car passes by the observer, he will hear the very tone that the siren actually makes. And when the car drives further and moves away rather than closer, the observer will hear a lower tone due to the lower frequency of the sound waves.

If the signal source moves towards the receiver (“observer”), that is, catches up with the wave emitted by it, then the wavelength decreases; if it moves away, the wavelength increases:

where co 0 is the angular frequency with which the source emits waves, c is the speed of propagation of waves in the medium, v is the speed of the wave source relative to the medium (positive if the source approaches the receiver and negative if it moves away).

Frequency recorded by a fixed receiver

Likewise, if the receiver moves towards the waves, it registers their crests more often and vice versa.

Mathematically, the time representation of the signal is the decomposition of the signal s(t), in which unit impulse functions - delta functions - are used as basic (fundamental) functions. The mathematical description of such a function is given by the relations

where 8(t) is a delta function different from zero at the origin (at t = 0).

For a more general case, when the delta function differs from zero at time t = tj (Fig. 1.9), we have

Rice. 1.9. Delta function

This mathematical model corresponds to an abstract impulse of infinitesimal duration and unlimited magnitude. The only parameter that correctly reflects the real signal is its duration. Using the delta function, you can express the value of the real signal s(t) at a specific time tji

This equality is valid for any current moment of time t.

Thus, the function s(t) can be expressed as a set of adjacent pulses of infinitesimal duration. The orthogonality of the set of such impulses is obvious, since they do not overlap in time.

The vast majority of signals used in modern communication systems are in the form of rectangular pulses. A rectangular pulse is only rectangular in the ideal case. In fact, it looks like the one shown in Fig. 1.10.

Rice. 1.10.

In the figure, the impulse has the following main components:

• - section t r t2 - front, i.e. voltage deviation from the initial level;
• - section t2-t3 - top of the pulse;
• - section t3-t 4 - cut (back edge), i.e. return of voltage to the original level.

Pulse parameters:

• 1. Pulse amplitude U m - the greatest deviation of the pulse from the initial level.
• 2. Pulse duration tn (t„). Measured at various levels of U m. The duration is:
  • - full, at the level of 0.lU m (t io);
  • - active, at which the pulse device is usually triggered - at the level of 0.5U m (t ia).
• 2. Front duration (1ph) - voltage rise time from 0.1 U m to 0.9 U m (can be full and active).
• 3. Cut duration (t c) - the time the voltage returns to its original level from 0.9U m to 0.lU m.
• 4. Decay of the top of the pulse (AU m). Described by the coefficient

recession The value of the decline coefficient ranges from 0.01 to 0.1.

As an additional parameter, we can note such a parameter as slope - the rate of rise (fall) of the pulse.

The front steepness is defined as

The slope of the cut is defined as

The slope is determined in [V/s]. A rectangular pulse has an infinitely large steepness. The most widely used are rectangular and exponential video pulses.

Sequences of pulses are used to transmit information - periodic and non-periodic. Periodic sequences are used only for testing equipment, and non-periodic sequences are used to transmit semantic information. However, to consider the basic patterns that occur during the transmission of information, let us turn to periodic sequences (Fig. 1.11).

Rice. 1.11.

Let's consider the parameters of the pulse sequence.

• 1. The period of repetition (repetition) is T. T = t„ + t n.
• 2. Repetition frequency (repetition) - F. This is the number of pulses per second. The expression for determining the frequency is: F = 1/T.
• 3. Duty factor - the ratio of the interval between pulses (period) (well) to the duration of the pulse itself (Q). Q=T/t H . The duty cycle is always greater than 1 (Q>1).
• 4. Duty factor - the reciprocal of the duty cycle (y).

Thus, the main parameters of pulses are amplitude, pulse duration, rise time, cutoff duration, and decay of the pulse top.

The parameters of the pulse sequence are the pulse repetition period, pulse repetition frequency, duty cycle, duty cycle.

A periodic signal is described by the expression s(t) = s(t + T), and during the period T (ti, t+ T) the signal is described by the formula

If during transmission the period T changes in an arbitrary manner, then the signal is called non-periodic. If the period T is repeated after a sufficiently large period of time, then the signal is called quasi-periodic or pseudo-random.

Among the many different signals, a special place is occupied by the so-called test or testing signals. The main ones are shown in Table 1.

Table 1

Test signals

The signals given in Table 1 are functions of time, but it should be noted that the same functions are also used in the frequency domain, where the argument is frequency. Any of the functions can be shifted in time to the desired region of the time plane and used to describe more complex signals.

The inclusion function (unit function (jump function) or Heaviside function) allows us to describe the process of transition of some physical object from the initial “zero” to the “unit” state, and this transition occurs instantly. Using the switching function it is convenient to describe, for example, various switching processes in electrical circuits.

When modeling signals and systems, the value of the unit function (jump function) at the point t = 0 is very often taken equal to 1, unless this is of fundamental importance. This function is also used to create mathematical models of finite duration signals. When any arbitrary function, including periodic, is multiplied by a rectangular pulse formed from two successive switching functions s(t) = o(t) - o(t - T), a section in the interval 0 - T is “cut out” from it, and function values ​​outside this interval are reset to zero (you should pay attention from the analytical record of this example, where these functions are “set”). The product of an arbitrary signal and the switching function characterizes the beginning of the signal.

The delta function or Dirac function by definition is further described by the following mathematical expressions:

moreover, the integral characterizes the fact that this function has a unit area and is localized at a specific time point.

The function S(t-i) is not differentiable, and has a dimension inverse to the dimension of its argument, which directly follows from the dimensionlessness of the integration result and, in accordance with the notes in the table, characterizes the rate of change of the inclusion function. The value of the delta function is zero everywhere except at point m, where it represents an infinitely narrow pulse with an infinitely large amplitude.

The delta function is a useful mathematical abstraction. In practice, such functions cannot be implemented with absolute accuracy, since it is impossible to realize an amplitude value equal to infinity at the point t = m on an analog time scale, i.e., defined in time also with infinite accuracy. But in all cases when the pulse area is equal to 1, the pulse duration is quite short, and during its action at the input of any system, the signal at its output practically does not change (the system’s response to the pulse is many times greater than the duration of the pulse itself), the input signal can be considered a unit impulse function with the properties of a delta function.

For all its abstractness, the delta function has a very definite physical meaning. Let's imagine a rectangular pulse signal (expressing it as a function from the table - this is a rect-function, i.e. signal s(t) = (1/ti)gesf(1-t)/ti], from English, rectangle - rectangle) duration t, the amplitude of which is equal to 1/t, and the area is correspondingly equal to 1.

As the value of the duration t decreases, the pulse, while decreasing in duration, retains its area equal to 1 and increases in amplitude. The limit of such an operation at m„->0u is called the delta pulse. This signal 5(t-x) is concentrated at one coordinate point t=x, the specific amplitude value of the signal is not determined, but the area (integral) remains equal to 1.

This is not the instantaneous value of the function at the point t = m, but an impulse (a force impulse in mechanics, a current impulse in electrical engineering, etc.)

n.) - a mathematical model of short action, the value of which is 1.

The delta function has filtering properties. Its essence is that if the delta function 5(t-x) is included in the integral of any function as a multiplier, then the result of integration is equal to the value of the integrand at point m of the location of the delta function, i.e.:

The limits of integration in this expression can be limited to the nearest neighborhoods of the point m.

When studying the general properties of signals, they abstract from their physical nature and purpose, replacing them with a mathematical model. A mathematical model is an approximate description of the signal in the form most suitable for the research being conducted. The mathematical description always reflects only the individual, most important properties of the signal that are essential for a given study.

The mathematical apparatus used in the analysis of signals allows for research without taking into account their physical nature.

In practical signal analysis, the representation in the form of a generalized Fourier series is most often used,

however, these signals must satisfy the condition of finite energy in the interval from t until t2

Since equality (1.10) is understood in the root-mean-square sense, representing the signal in the form of a generalized Fourier series reduces to choosing a system of basis functions (

Currently, the following orthogonal basis functions are widely used - trigonometric (sinx, cosx), Chebyshev, Hermite polynomials, Walsh, Haar functions, etc.

The coefficients c n are determined based on the minimization of the root mean square error a 0 caused by the finite number of terms on the right side of expression (1.10)

where N is the number of terms, and since the basis functions (p p depend on time.

In this case, the error caused by the finite number of terms on the right side of expression (1.10) is the smallest in comparison with other methods of determining coefficients with n. Since a > 0, the inequality Г31 always holds

2.1.1.Deterministic and random signals

Deterministic signal is a signal whose instantaneous value at any time can be predicted with a probability equal to one.

An example of a deterministic signal (Fig. 10) can be: sequences of pulses (the shape, amplitude and time position of which are known), continuous signals with given amplitude-phase relationships.

Methods for specifying a MM signal: analytical expression (formula), oscillogram, spectral representation.

An example of a MM of a deterministic signal.

s(t)=S m ·Sin(w 0 t+j 0)

Random signal– a signal whose instantaneous value at any time is unknown in advance, but can be predicted with a certain probability, less than one.

An example of a random signal (Fig. 11) could be a voltage corresponding to human speech or music; sequence of radio pulses at the input of the radar receiver; interference, noise.

2.1.2. Signals used in radio electronics

Continuous in magnitude (level) and continuous in time (continuous or analog) signals– take any values ​​s(t) and exist at any moment in a given time interval (Fig. 12).

Continuous in magnitude and discrete in time signals are specified at discrete time values ​​(on a countable set of points), the magnitude of the signal s(t) at these points takes on any value in a certain interval along the ordinate axis.

The term “discrete” characterizes the method of specifying a signal on the time axis (Fig. 13).

Magnitude-quantized and time-continuous signals are specified on the entire time axis, but the value s(t) can only take discrete (quantized) values ​​(Fig. 14).

Magnitude-quantized and time-discrete (digital) signals– signal level values ​​are transmitted in digital form (Fig. 15).

2.1.3. Pulse signals

Pulse- an oscillation that exists only within a finite period of time. In Fig. 16 and 17 show a video pulse and a radio pulse.

For a trapezoidal video pulse, enter the following parameters:

A – amplitude;

t and – video pulse duration;

t f – front duration;

t cf – cut duration.

S р (t)=S in (t)Sin(w 0 t+j 0)

S in (t) – video pulse – envelope for a radio pulse.

Sin(w 0 t+j 0) – filling the radio pulse.

2.1.4. Special signals

Switching function (single function(Fig. 18) or Heaviside function) describes the process of transition of some physical object from a “zero” to a “unit” state, and this transition occurs instantly.

Delta function (Dirac function) is a pulse whose duration tends to zero, while the height of the pulse increases indefinitely. It is customary to say that the function is concentrated at this point.

	(2)
	(3)

Questions for the state exam

course "Digital signal processing and signal processors"

(Korneev D.A.)

Correspondence studies

Classification of signals, energy and power of signals. Fourier series. Sine-cosine form, real form, complex form.

CLASSIFICATION OF SIGNALS USED IN RADIO ENGINEERING

From an information point of view, signals can be divided into deterministic And random.

Deterministic call any signal whose instantaneous value at any time can be predicted with probability one. Examples of deterministic signals include pulses or bursts of pulses, the shape, amplitude and time position of which are known, as well as a continuous signal with specified amplitude and phase relationships within its spectrum.

TO random refer to signals whose instantaneous values ​​are unknown in advance and can be predicted only with a certain probability less than one. Such signals are, for example, electrical voltage corresponding to speech, music, a sequence of telegraph code characters when transmitting non-repeating text. Random signals also include a sequence of radio pulses at the input of a radar receiver, when the amplitudes of the pulses and the phases of their high-frequency filling fluctuate due to changes in propagation conditions, target position and some other reasons. There are many other examples of random signals that can be given. Essentially, any signal that carries information should be considered random.

The deterministic signals listed above, “fully known,” no longer contain information. In the following, such signals will often be referred to as oscillations.

Along with useful random signals, in theory and practice we have to deal with random interference - noise. The noise level is the main factor limiting the speed of information transmission for a given signal.

Analog signal Discrete signal

Quantized signal Digital signal

Rice. 1.2. Signals arbitrary in magnitude and time (a), arbitrary in magnitude and discrete in time (b), quantized in magnitude and continuous in time (c), quantized in magnitude and discrete in time (d)

Meanwhile, signals from the message source can be either continuous or discrete (digital). In this regard, the signals used in modern radio electronics can be divided into the following classes:

arbitrary in value and continuous in time (Fig. 1.2, a);

arbitrary in value and discrete in time (Fig. 1.2, b);

quantized in magnitude and continuous in time (Fig. 1.2, c);

quantized in magnitude and discrete in time (Fig. 1.2, d).

First class signals (Fig. 1.2, a) are sometimes called analog, since they can be interpreted as electrical models of physical quantities, or continuous, since they are specified along the time axis at an uncountable set of points. Such sets are called continuum. In this case, along the ordinate axis, signals can take on any value within a certain interval. Since these signals may have discontinuities, as in Fig. 1.2, and, then, in order to avoid incorrectness in the description, it is better to designate such signals by the term continuum.

So, the continuous signal s(t) is a function of the continuous variable t, and the discrete signal s(x) is a function of the discrete variable x, which takes only fixed values. Discrete signals can be created directly by the source of information (for example, discrete sensors in control or telemetry systems) or formed as a result of sampling of continuous signals.

In Fig. 1.2, b shows a signal specified at discrete values ​​of time t (at a countable set of points); the magnitude of the signal at these points can take any value in a certain interval along the ordinate axis (as in Fig. 1.2, a). Thus, the term discrete characterizes not the signal itself, but the way it is specified on the time axis.

Signal in Fig. 1.2, is specified on the entire time axis, but its value can only take discrete values. In such cases, we speak of a signal quantized by level.

In what follows, the term discrete will be used only in relation to time sampling; discreteness in level will be designated by the term quantization.

Quantization is used when representing signals in digital form using digital encoding, since levels can be numbered with numbers with a finite number of digits. Therefore, a signal discrete in time and quantized in level (Fig. 1.2, d) will henceforth be called digital.

Thus, it is possible to distinguish between continuous (Fig. 1.2, a), discrete (Fig. 1.2, b), quantized (Fig. 1.2, c) and digital (Fig. 1.2, d) signals.

Each of these signal classes can be associated with an analog, discrete or digital circuit. The relationship between the type of signal and the type of circuit is shown in the functional diagram (Fig. 1.3).

When processing a continuum signal using an analog circuit, no additional signal conversion is required. When processing a continuum signal using a discrete circuit, two transformations are necessary: ​​sampling the signal in time at the input of the discrete circuit and the inverse transformation, i.e., restoring the continuum structure of the signal at the output of the discrete circuit.

For an arbitrary signal s(t) = a(t)+jb(t), where a(t) and b(t) are real functions, the instantaneous signal power (energy distribution density) is determined by the expression:

w(t) = s(t)s*(t) = a 2 (t)+b 2 (t) = |s(t)| 2.

The signal energy is equal to the integral of the power over the entire interval of the signal's existence. In the limit:

E s = w(t)dt = |s(t)| 2 dt.

Essentially, instantaneous power is the power density of a signal, since power measurements are only possible through the energy released over certain intervals of non-zero length:

w(t) = (1/Dt) |s(t)| 2 dt.

The signal s(t) is studied, as a rule, over a certain interval T (for periodic signals - within one period T), with the average signal power:

W T (t) = (1/T) w(t) dt = (1/T) |s(t)| 2 dt.

The concept of average power can also be extended to continuous signals, the energy of which is infinitely large. In the case of an unlimited interval T, a strictly correct determination of the average signal power is made using the formula:

W s = w(t) dt.

The idea that any periodic function can be represented as a series of harmonically related sines and cosines was proposed by Baron Jean Baptiste Joseph Fourier (1768−1830).

Fourier series function f(x) is represented as

Before starting to study any phenomena, processes or objects, science always strives to classify them according to as many characteristics as possible. Let us make a similar attempt in relation to radio signals and interference.

Basic concepts, terms and definitions in the field of radio signals are established by the state standard “Radio signals. Terms and definitions". Radio signals are very diverse. They can be classified according to a number of characteristics.

1. It is convenient to consider radio signals in the form of mathematical functions specified in time and physical coordinates. From this point of view, signals are divided into one-dimensional And multidimensional. In practice, one-dimensional signals are most common. They are usually functions of time. Multidimensional signals consist of many one-dimensional signals, and in addition, reflect their position in n- dimensional space. For example, signals that carry information about the image of an object, nature, person or animal are functions of both time and position on the plane.

2. According to the peculiarities of the structure of temporary representation, all radio signals are divided into analog, discrete And digital. Lecture No. 1 has already discussed their main features and differences from each other.

3. According to the degree of availability of a priori information, the entire variety of radio signals is usually divided into two main groups: deterministic(regular) and random signals. Deterministic are radio signals whose instantaneous values ​​are reliably known at any time. An example of a deterministic radio signal is a harmonic (sinusoidal) oscillation, a sequence or burst of pulses, the shape, amplitude and temporal position of which are known in advance. In fact, a deterministic signal does not carry any information and almost all of its parameters can be transmitted over a radio communication channel using one or more code values. In other words, deterministic signals (messages) essentially do not contain information, and there is no point in transmitting them. They are usually used to test communication systems, radio channels or individual devices.

Deterministic signals are divided into periodic And non-periodic (pulse). A pulse signal is a signal of finite energy, significantly different from zero during a limited time interval commensurate with the time of completion of the transient process in the system on which this signal is intended to influence. There are periodic signals harmonic, that is, containing only one harmonic, and polyharmonic, the spectrum of which consists of many harmonic components. Harmonic signals include signals described by a sine or cosine function. All other signals are called polyharmonic.

Random signals– these are signals whose instantaneous values ​​at any time are unknown and cannot be predicted with a probability equal to one. Paradoxical as it may seem at first glance, only a random signal can be a signal carrying useful information. The information in it is contained in a variety of amplitude, frequency (phase) or code changes in the transmitted signal. In practice, any radio signal containing useful information should be considered random.

4. In the process of transmitting information, signals can be subjected to one or another transformation. This is usually reflected in their name: signals modulated, demodulated(detected), coded (decoded), reinforced, detainees, sampled, quantized etc.

5. According to the purpose that the signals have during the modulation process, they can be divided into modulating(the primary signal that modulates the carrier wave) or modulated(carrier vibration).

6. According to belonging to one or another type of information transmission systems, they distinguish telephone, telegraph, broadcasting, television, radar, managers, measuring and other signals.

Let us now consider the classification of radio interference. Under radio interference understand a random signal, homogeneous with the useful one and acting simultaneously with it. For radio communication systems, interference is any accidental effect on a useful signal that impairs the fidelity of the reproduction of transmitted messages. Classification of radio interference is also possible according to a number of criteria.

1. Based on the location of occurrence, interference is divided into external And internal. Their main types have already been discussed in lecture No. 1.

2. Depending on the nature of the interaction of interference with the signal, they are distinguished additive And multiplicative interference. Additive is interference that is added to the signal. Multiplicative is a noise that is multiplied with a signal. In real communication channels, both additive and multiplicative interference usually occur.

3. Based on their basic properties, additive interference can be divided into three classes: concentrated along the spectrum(narrowband interference), impulse noise(focused in time) and fluctuation noise(fluctuation noise), not limited either in time or spectrum. Spectrum-concentrated interference is when the bulk of its power is located in certain parts of the frequency range that are smaller than the bandwidth of the radio system. Pulse interference is a regular or chaotic sequence of pulse signals that are homogeneous with the useful signal. The sources of such interference are digital and switching elements of radio circuits or devices operating near them. Pulsed and concentrated interference are often called tips.

There is no fundamental difference between signal and noise. Moreover, they exist in unity, although they are opposite in their action.