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 electrical currents or voltages that change over time.

All electrical signals are divided by deterministic and random.

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

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

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

Random signal - it is a random process that changes in a given dynamic range and takes 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 a 2) do not depend on time. Otherwise, the process is not stationary.

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

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 sufficient to average a random signal over an ensemble of realizations or over time.

Real signals are always random to some extent. First, the signal is always distorted in the transmitter and receiver circuits due to the random nature of the change in the parameters of their elements. Secondly, in the transmission medium, the signal is always affected by random interference, turning it into a random one at the input of the receiver. At the same time, in many cases, a real signal with a certain degree of accuracy can be regarded 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 time interval T, called the 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 rate.

If during transmission T changes in an arbitrary way, then the signal is called non-periodic. If the period T repeats after a sufficiently long time interval, then the signal is called quasiperiodic or pseudo-random.

Signals, even analog ones, existing only in one time interval, are pulsed. Figure 1.7 shows some of the types of signals listed above.

Rice. 1.7, a describes, for example, a deterministic discrete signal with a repetition period of rectangular pulses T and a pulse duration T s in a 2: 1 ratio (meander). The ratio Q = T / T s is called the duty cycle of the signal. For the signal in Fig. 1.7, and it is equal to 2, and for the signal in Fig. 1.7, s - 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 only one impulse is selected in all the figures, then we will receive, respectively, an impulse signal.

Rice. 1.7.

When considering various signals, one usually resorts to four types of their representation:

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

Temporary submission.

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

Rice. 1.8.

Let us assume that the "observer" is at a point that is characterized by the observation interval t4 - ts. Obviously, at the moment of 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 we approach the "observer", the signal begins to stretch in time and we see some of its structure (time interval t2 - At this interval, the signal structure corresponds to its true structure, but the pulse repetition rate will not correspond to the actual one. interval t 4 - t 5, when the location of the signal will correspond 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 passes by the observer. Suppose the siren emits 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 emits. But if the car approaches the observer, the frequency of the sound waves will increase, and the observer will hear a higher pitch than the siren actually sounds. The moment the car drives past the observer, he will hear the very tone that the siren actually sounds. And when the car goes further and is already moving away, and not approaching, the observer will hear a lower tone, due to the lower frequency of sound waves.

If the signal source moves towards the receiver ("observer"), that is, it catches up with the wave it emits, then the wavelength decreases, if it moves away, the wavelength increases:

where ω 0 is the angular frequency with which the source emits waves, c is the speed of wave propagation 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 temporal 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 nonzero delta function 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

Such a mathematical model corresponds to an abstract impulse of infinitely short duration and infinite 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 particular 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 adjoining pulses of infinitely short duration. The orthogonality of the aggregate 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. The rectangular impulse is rectangular only 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 - the top of the impulse;
• - section t3-t 4 - cut (trailing edge), i.e. return of voltage to the original level.

Pulse parameters:

• 1. The amplitude of the impulse U m is the greatest deviation of the impulse from the initial level.
• 2. The duration of the impulse tn (t „). Measured at different levels U m. The duration is:
  • - complete, at the level 0, lU m (mio);
  • - active, at which the impulse device is usually triggered - at the level of 0.5U m (t ua).
• 2. Front duration (1ph) - voltage rise time from 0.1 U m to 0.9 U m (can be full and active).
• 3. Cutoff duration (t c) - time of voltage return to the initial level from 0.9U m to 0, lU m.
• 4. Decline of the top of the impulse (AU m). Described by the coefficient

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

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

The steepness of the front is defined as

The steepness of the cut is defined as

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

To transmit information, pulse sequences are used - periodic and non-periodic. Periodic sequences are used only for hardware testing, and non-periodic sequences are used to transmit semantic information. Nevertheless, to consider the basic patterns that take place in the transmission of information, let us turn to periodic sequences (Fig. 1.11).

Rice. 1.11.

Consider the parameters of the pulse train.

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

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

The parameters of the pulse sequence are the pulse repetition rate, pulse repetition rate, 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 the transmission, the period T changes in an arbitrary manner, then the signal is called non-periodic. If the period T repeats after a sufficiently long time interval, then the signal is called quasiperiodic or pseudo-random.

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

Table 1

Test signals

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

The inclusion function (unit function (jump function) or Heaviside function) allows to describe the process of transition of some physical object from the initial - "zero" to "single" state, and this transition occurs instantly. With the help of the switch-on function, it is convenient to describe, for example, various switching processes in electrical circuits.

When simulating signals and systems, the value of the unit function (jump function) at the point t = 0 is very often taken equal to 1, if this is not of fundamental importance. This function is also used to create mathematical models of signals of finite duration. When any arbitrary function, including a periodic one, is multiplied by a rectangular pulse formed from two successive switching functions s (t) = o (t) - o (t - T), a section is “cut out” from it on the interval 0 - T, and the values ​​of the function are zeroed outside this interval (you should pay attention from the analytical record of this example, where these functions are "exposed"). The product of an arbitrary signal and the switch-on function characterizes the onset of the signal.

The delta function or Dirac function, by definition, is additionally 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 table notes, characterizes the rate of change of the switch-on function. The value of the delta function is zero everywhere except at the point m, where it is an infinitely narrow pulse with an infinitely large amplitude.

The delta function is a useful mathematical abstraction. In practice, such functions cannot be realized with absolute accuracy, since it is impossible to realize an amplitude value equal to infinity at the point t = t on an analog time scale, i.e., determined in time also with infinite accuracy. But in all cases when the pulse area is equal to 1, the pulse duration is rather short, and during its operation 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 pulse duration), the input signal can be considered a unit impulse function with delta-function properties.

For all its abstractness, the delta function has a definite physical meaning. Imagine a rectangular pulse signal (expressing it with a function from the table - this is a rect-function, that is, the signal s (t) = (1 / ty) hesf (1-t) / ty], from English, rectangle is a rectangle) duration m, "the amplitude of which is 1 / m," and the area, respectively, is equal to 1.

With a decrease in the value of the duration t and the pulse, decreasing in duration, retains its area equal to 1, and increases in amplitude. The limit of such an operation at m „-> 0 and is called the delta-pulse. This signal 5 (t-x) is concentrated in 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 = t, but the impulse (impulse of force in mechanics, impulse of current in electrical engineering, etc.)

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

The delta function has a filtering property. Its essence lies in the fact that if the delta function 5 (t-x) enters into the integral of any function as a factor, then the result of integration is equal to the value of the integrand at the 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 a signal in the form most suitable for the research being carried out. The mathematical description always reflects only some of the most important properties of the signal that are essential for a given study.

The mathematical apparatus used in the analysis of signals makes it possible to carry out research without taking into account their physical nature.

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

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

Since equality (1.10) is understood in the root-mean-square sense, the representation of the signal in the form of a generalized Fourier series is reduced to the choice of 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 with n are determined proceeding from the minimization of the root-mean-square error a 0 due to a finite number of terms on the right-hand 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 a finite number of terms on the right-hand side of expression (1.10) is the smallest in comparison with other methods for determining the coefficients with n. Since a> 0, the inequality Г31

Before embarking on the study of any new phenomena, processes or objects, science always strives to classify them according to the largest possible attributes. For consideration and analysis of signals, let us single out their main classes. This is necessary for two reasons. First, checking the belonging of a signal to a specific class is an analysis procedure. Secondly, to represent and analyze signals of different classes, it is often necessary to use different means and approaches. Basic concepts, terms and definitions in the field of radio technical signals are established by the national (previously, state) standard “Radio technical signals. Terms and Definitions". Radio signals are extremely diverse. A part of the brief classification of signals according to a number of features is shown in Fig. 1. More detailed information about a number of concepts is presented below. It is convenient to consider radio-technical signals in the form of mathematical functions given in time and physical coordinates. From this point of view, signals are usually described by one (one-dimensional signal; n = 1), two

(two-dimensional signal; n = 2) or more (multidimensional signal n> 2) independent variables. One-dimensional signals are functions of time only, and multidimensional, in addition, reflect the position in n-dimensional space.

Fig. 1. Classification of radio engineering signals

For definiteness and simplification, we will mainly consider one-dimensional signals that depend on time, however, the material of the textbook admits generalization to the multidimensional case, when the signal is represented as a finite or infinite set of points, for example, in space, the position of which depends on time. In television systems, a black-and-white image signal can be viewed as a function f (x, y, f) of two spatial coordinates and time, representing the radiation intensity at a point (x, y) at time t at the cathode. When transmitting a color television signal, we have three functions f (x, y, t), g (x, y, t), h (x, y, t), defined on a three-dimensional set (these three functions can also be considered as components of a three-dimensional vector fields). In addition, various types of television signals can occur when a television image is transmitted together with sound.

A multidimensional signal is an ordered collection of one-dimensional signals. A multidimensional signal is created, for example, by a system of voltages at the terminals of a multipole (Fig. 2). Multidimensional signals are described by complex functions, and their processing is often possible in digital form. Therefore, multidimensional signal models are especially useful in cases where the functioning of complex systems is analyzed using computers. So, multidimensional, or vector, signals consist of many one-dimensional signals

where n is an integer, the dimension of the signal.

R
is. 2. Multipole voltage system

According to the peculiarities of the structure of the temporal representation (Fig. 3), all radio technical signals are divided into analog (analog), discrete (discrete-time; from Latin discretus - divided, intermittent) and digital (digital).

If the physical process generating a one-dimensional signal can be represented by a continuous function of time u (t) (Fig. 3, a), then such a signal is called analog (continuous), or, more generally, continuous (continuos - multistage), if the latter has jumps , discontinuities along the amplitude axis. Note that traditionally the term "analog" is used to describe signals that are continuous in time. A continuous signal can be interpreted as a real or complex oscillation in time u (t), which is a function of a continuous real time variable. The concept of "analog" signal is related to the fact that its any instantaneous value is similar to the law of variation of the corresponding physical quantity in time. An example of an analog signal is some voltage that is applied to the input of an oscilloscope, resulting in a continuous curve on the screen as a function of time. Since modern CW signal processing using resistors, capacitors, operational amplifiers, and the like has little in common with analog computers, the term “analog” does not seem entirely unfortunate today. It would be more correct to call continuous signal processing what is commonly referred to today as analog signal processing.

In radio electronics and communications technology, pulse systems, devices and circuits are widely used, the operation of which is based on the use of discrete signals. For example, an electrical signal reflecting speech is continuous both in level and in time, and a temperature sensor, which outputs its values ​​every 10 minutes, serves as a source of signals that are continuous in value, but discrete in time.

A discrete signal is obtained from an analog signal by means of a special conversion. The process of converting an analog signal into a sequence of samples is called sampling, and the result of this conversion is a discrete signal or discrete series.

The simplest mathematical model of a discrete signal
- a sequence of points on the time axis, taken, as a rule, at regular intervals
, called the sampling period (or interval, sampling step; sample time), and in each of which the values ​​of the corresponding continuous signal are set (Fig. 3, b). The reciprocal of the sampling period is called the sampling frequency:
(another designation
). The corresponding angular (circular) frequency is determined as follows:
.

Discrete signals can be created directly by a source of information (in particular, discrete readouts of sensor signals in control systems). The simplest example of discrete signals is the temperature information broadcast in radio and television news programs, but there is usually no weather information in the pauses between such broadcasts. Do not think that discrete messages are necessarily converted into discrete signals, and continuous messages - into continuous signals. Most often, it is continuous signals that are used to transmit discrete messages (as their carriers, i.e., a carrier). Discrete signals can be used to transmit continuous messages.

Obviously, in the general case, the representation of a continuous signal by a set of discrete samples leads to a certain loss of useful information, since we do not know anything about the behavior of the signal in the intervals between samples. However, there is a class of analog signals for which such a loss of information practically does not occur, and therefore they can be reconstructed with a high degree of accuracy from the values ​​of their discrete samples.

A kind of discrete signals is a digital signal.In the process of converting discrete samples of a signal into digital form (usually into binary numbers), it is quantized by the level (quantization) of the voltage ... In this case, the values ​​of the signal levels can be numbered with binary numbers with a finite required number of digits. A signal that is discrete in time and quantized in level is called a digital signal. By the way, signals quantized in level but continuous in time are rarely encountered in practice. In a digital signal, discrete signal values
first, they are quantized according to the level (Fig. 3, c) and then the quantized samples of the discrete signal are replaced with numbers
most often implemented in binary code, which is represented by high (one) and low (zero) levels of voltage potentials - short pulses of duration (Fig. 3, d). This code is called unipolar. Since the samples can take a finite set of voltage levels (see, for example, the second sample in Fig. 3, d, which in digital form can almost equally be written as the number 5 - 0101, and the number 4 - 0100), then when presenting a signal, it is inevitable it is rounded off. The resulting round off errors are called quantization error (quantization noise).

The sequence of numbers that represent a digitally processed signal is a discrete series. The numbers that make up the sequence are signal values ​​at separate (discrete) times and are called digital signal samples (samples). Further, the quantized signal value is represented as a set of pulses characterizing zeros ("0") and ones ("1") when this value is represented in the binary number system (Fig. 3d). The set of pulses is used to amplitude modulate the carrier wave and obtain a pulse-code radio signal.

As a result of digital processing, nothing "physical" is obtained, only numbers. And numbers are an abstraction, a way of describing the information contained in a message. Therefore, we need to have something physical that will represent the numbers or "be the carrier" of the numbers. So, the essence of digital processing is that a physical signal (voltage, current, etc.) is converted into a sequence of numbers, which is then subjected to mathematical transformations in a computing device.

The transformed digital signal (sequence of numbers), if necessary, can be converted back to voltage or current.

Digital signal processing provides ample opportunities for the transmission, reception and transformation of information, including those that cannot be implemented using analog technology. In practice, when analyzing and processing signals, digital signals are most often replaced by discrete ones, and their difference from digital ones is interpreted as quantization noise. In this regard, the effects associated with level quantization and digitization of signals in most cases will not be taken into account. We can say that discrete signals are processed both in discrete and digital circuits (in particular, in digital filters), only within the structure of digital circuits these signals are represented by numbers.

Computing devices designed for signal processing can operate with digital signals. There are also devices built mainly on the basis of analog circuitry, which work with discrete signals presented in the form of pulses of different amplitudes, durations or repetition rates.

One of the main features by which signals are distinguished is the predictability of the signal (its values) over time.

R
is. 3. Radio technical signals:

a - analog; b - discrete; в - quantized; d - digital

According to the mathematical representation (according to the degree of availability of a priori, from Latin a priori - from the previous, that is, pre-experimental information), it is customary to divide all radio-technical signals into two main groups: deterministic (regular; determined) and random (casual) signals (Fig. 4).

Radio-technical signals are called deterministic, the instantaneous values ​​of which at any moment of time are reliably known, that is, predictable with a probability equal to one. Deterministic signals are described by predetermined functions of time. By the way, the instantaneous value of a signal is a measure of how much and in what direction the variable deviates from zero; thus, the instantaneous values ​​of the signal can be both positive and negative (Fig. 4, a). The simplest examples of a deterministic signal are harmonic oscillations with a known initial phase, high-frequency oscillations modulated according to a known law, a sequence or burst of pulses, the shape, amplitude and time position of which are known in advance.

If the message transmitted through the communication channels were deterministic, that is, known in advance with full reliability, then its transmission would be meaningless. Such a deterministic message, in fact, does not contain any new information. Therefore, messages should be considered as random events (or random functions, random variables). In other words, there should be a number of message options (for example, many different pressure values ​​given by the sensor), of which one is realized with a certain probability. In this regard, the signal is also a random function. A deterministic signal cannot be a carrier of information. It can be used only for testing a radio-technical information transmission system or testing its individual devices. The random nature of messages, as well as interference, determined the crucial importance of the theory of probability in the construction of the theory of information transmission.

Rice. 4. Signals:

a - deterministic; b - random

Deterministic signals are divided into periodic and non-periodic (impulse). A final energy signal that is substantially different from zero for a limited time interval commensurate with the time of completion of the transient in the system for which it is intended to act is called a pulse signal.

Signals are called random if their instantaneous values ​​are not known at any moment and cannot be predicted with a probability equal to one. In fact, for random signals, you can only know the probability that it will take on any value.

It may seem that the concept of "random signal" is not entirely correct.

But this is not the case. For example, the voltage at the output of the receiver of a thermal imager, directed to the source of infrared radiation, represents chaotic oscillations that carry various information about the analyzed object. Strictly speaking, all signals encountered in practice are random and most of them represent chaotic functions of time (Fig. 4, b). Paradoxical as it may seem at first glance, only a random signal can be a signal carrying useful information. Information in such a signal is embedded in a variety of amplitude, frequency (phase) or code changes in the transmitted signal. Communication signals in time change instantaneous values, and these changes can be predicted only with a certain probability, less than one. Thus, communication signals are in some way random processes, therefore, their description is carried out by means of methods similar to the methods of describing random processes.

In the process of transmitting useful information, radio signals can be subjected to one or another transformation. This is usually reflected in their name: signals are modulated, demodulated (detected), encoded (decoded), amplified, delayed, sampled, quantized, etc.

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

By belonging to one or another type of radio engineering systems, and in particular information transmission systems, distinguish between "communication", telephone, telegraph, radio broadcasting, television, radar, radio navigation, measuring, control, service (including pilot signals) and other signals ...

The given short classification of radio-technical signals does not fully cover all their diversity.

Before embarking on the study of any phenomena, processes or objects, science always strives to classify them according to the largest possible number of signs. Let's make a similar attempt in relation to radio signals and interference.

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

1. It is convenient to consider radio-technical signals in the form of mathematical functions given in time and physical coordinates. From this point of view, the 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 carrying information about the image of an object, nature, man or animal, are functions of both time and position on the plane.

2. According to the peculiarities of the structure of the temporal representation, all radio technical signals are subdivided into analog, discrete and digital... In lecture number 1, their main features and differences from each other have already been considered.

3. According to the degree of availability of a priori information, it is customary to divide the entire variety of radio-technical signals into two main groups: deterministic(regular) and random signals. Radio-technical signals are called deterministic, the instantaneous values ​​of which are reliably known at any time. An example of a deterministic radio engineering 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 via a radio communication channel with 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 subdivided into periodic and non-periodic (impulse). An impulse signal is a signal of final energy that is significantly different from zero for a limited time interval commensurate with the time of completion of the transient in the system for which this signal is intended to act. Periodic signals are harmonic, that is, containing only one harmonic, and polyharmonic, the spectrum of which consists of many harmonic components. Harmonic signals are signals described by a sine or cosine function. All other signals are called polyharmonic.

Random signals- these are signals, the instantaneous values ​​of which are unknown at any moments of time 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 embedded 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, discretized, quantized and etc.

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

6. By belonging to one or another type of information transmission systems are distinguished telephone, telegraph, broadcasting, television, radar, managing directors, measuring and other signals.

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

1. At the place of occurrence, the interference is divided into external and internal... Their main types have already been discussed in lecture number 1.

2. Depending on the nature of the interaction of the interference with the signal, one distinguishes additive and multiplicative interference. Interference is called additive, which is added to the signal. Interference is called multiplicative interference, which is multiplied with the signal. In real communication channels, both additive and multiplicative interference usually take place.

3. According to its main properties, additive noise can be divided into three classes: spectrum-lumped(narrowband interference), impulse noise(centered in time) and fluctuation noise(fluctuation noise), not limited in time or spectrum. Spectrum-centered interference is called interference, the bulk of the power of which is located in separate parts of the frequency range, less than the bandwidth of the radio engineering system. Pulse noise is a regular or chaotic sequence of pulsed signals that are homogeneous with a useful signal. Sources of such interference are digital and switching elements of radio circuits or devices operating near them. Pulsed and lumped disturbances are often referred to as tips.

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

General information about radio signals

When transmitting information over a distance using radio engineering systems, various types of radio engineering (electrical) signals are used. Traditionally radio engineering signals are considered to be any electrical signals related to the radio band. From a mathematical point of view, any radio signal can be represented by a certain function of time u (t ), which characterizes the change in its instantaneous values ​​of voltage (most often), current or power. According to the mathematical representation, the whole variety of radio engineering signals is usually divided into two main groups: deterministic (regular) and random signals.

Deterministic are called radio technical signals, the instantaneous values ​​of which are reliably known at any moment of time, that is, they are predictable with a probability equal to one / 1 /. An example of a deterministic radio engineering signal is a harmonic oscillation. It should be noted that, in fact, a deterministic signal does not carry any information and almost all of its parameters can be transmitted via a radio communication channel with one or more code values. In other words, deterministic signals (messages) essentially do not contain information, and there is no point in transmitting them.

Random signals- these are signals, the instantaneous values ​​of which at any time instant are not known and cannot be predicted with a probability equal to one / 1 /. Almost all real random signals, or most of them, are chaotic functions of time.

According to the peculiarities of the structure of the temporal representation, all radio technical signals are divided into continuous and discrete.and by the type of transmitted information: analog and digital.In radio engineering, pulse systems are widely used, the operation of which is based on the use of discrete signals. One of the types of discrete signals is digital signal / 1 /. In it, discrete signal values ​​are replaced by numbers, most often implemented in a binary code, which represent high (unit) and low (zero) voltage potential levels.

Functions describing signals can take both real and complex values. Therefore, in radio engineering, one speaks of real and complex signals. Application of this or that form of signal description is a matter of mathematical convenience.

Spectrum concept

Direct analysis of the effect of signals of complex shape on radio circuits is very difficult and generally not always possible. Therefore, it makes sense to represent complex signals as the sum of some simple elementary signals. The principle of superposition substantiates the possibility of such a representation, asserting that in linear circuits, the effect of the total signal is equivalent to the sum of the effects of the corresponding signals separately.

Harmonics are often used as elementary signals. This choice has several advantages:

a) Decomposition into harmonics is realized quite easily by using the Fourier transform.

b) When a harmonic signal acts on any linear circuit, its shape does not change (remains harmonic). The signal frequency is also saved. Amplitude and phase vary, of course; they can be calculated relatively simply using the method of complex amplitudes.

c) In technology, resonant systems are widely used, which make it possible to experimentally separate one harmonic from a complex signal.

Representing a signal as a sum of harmonics given by frequency, amplitude, and phase is called signal spectrum decomposition.

The harmonics that make up the signal are given in trigonometric or imaginary indicative form.