The correct term is “simple” signal, such as a radio pulse with a simple form and high-frequency vibrations of constant frequency that are universally accepted. For simple signals, additional spectrum width A/ trivality At, tobto. the base of signal B is equal to the amount of money occupied by signal B, a value close to “1”:
Zokrema, a direct-circuit pulse with a constant frequency of replenishment is brought to the class of simple signals, which is why for the new A/*“ /x ta; At = t b, And, therefore, the mind is reduced (4.11).
Signals, which are in addition to their trivality on the spectrum width, then. the base, which significantly moves the unit (B >> 1), was called “folding” (folding signals).
To increase the potential accuracy of radar range measurements, it is necessary to analyze signals with a wide spectrum. When limiting the peak intensity of the pulse, in order to save the range of the RTS, completely expand the spectrum of the probing signal not by shortening it, but by introducing internal pulse phase or frequency modulation, . go beyond the rakhunok to the folding signals.
Radio pulse with linear frequency modulation
Radar has widely varying linear-frequency-modulated (chirp) pulse signals, the frequency of which can be represented in the form:
de/0 - coarse frequency value; D/d-frequency deviation; t i – the severity of the impulse. The linear law of frequency change (4.12) is confirmed by the quadratic law of phase change for the chirp signal:
The chirp pulse has a rectangular shape, shown in Fig. 4.9, the complex picture looks like this:
Small 4.9.
The standardized function of inconvenience looks like this:
This function describes the relief of the body of the insignificance of the direct-cut chirp pulse, through which the vertical plane Q = 0 - resulting in the chirp pulse at the output of a special filter depending on the frequency discord. This graph is shown in Fig. 4.10 along the line. For leveling, a straight line shows the remaining forward-cut radio pulse with a constant frequency of filling and trivality tn at the UV output. As is obvious from this little one, when the chirp pulse passes through the SF, the second hour is reached. If at the input of the filter the impulse has a trivality t,„ = t i, then at the output the trivality of the pulse becomes x osh= t (1 TO d 2.47g (Beyond 0.5). So the coefficient is constrained
Small 4.10.
The compression coefficient is directly proportional to the frequency deviation. The impulse disturbance and frequency deviation can be placed independently of each other, allowing for a high compression ratio to be realized.
Fragments DO l "DO, DO - the width of the spectrum of the chirp pulse, the compression ratio (15.15) appears to be practically equal to the base signal S&B(this is expanded across all folded signals). The folding signal behind the additional UV can be squeezed by the trivality by an amount that is similar to the base of the signal.
Let us explain the compression of the chirp signal in the UV. The chirp signal shown in Fig. 4.9 demonstrates a useful filter with impulse characteristics (Fig. 4.11). The impulse characteristic will interfere with the system's input into the delta pulse. At the output of the filter, presumably before the digestion procedure in the pulse reaction, the warehouses initially appear to be of higher frequency, and then of lower frequency. High-frequency stores are blocked by the filter by less low-frequency ones. The lower frequencies of the chirp pulse arrive at the input of the SF earlier (div. Fig. 4.9), but are not overshadowed by the larger world; The highest frequencies appear later and are less affected. As a result, groups of different frequencies are brought together and the pulse is shortened.
Small 4.11.
As a filter, shading lines (LZ) are installed on the surface acoustic coils (PAR). At the input and output of the LZ, the installed pin transformers (IDCs) convert the energy of the electric field into mechanical energy and back. For different frequencies, the width of the sound pipeline and high-frequency warehouses adjust the low frequencies. Tim himself realizes the compression of chirp pulses.
More than allowed chirp pulses per hour and frequency to operate significantly more complexly, but also allowed these pulses themselves in one of the parameters (with a given value of the other parameter). This results from the diagrams of insignificance of the chirp radio pulse (Fig. 4.12). Fig – 41 2. Diagram
^ insignificance
The complete separation of signals per hour, chirp pulse duration and frequency is possible, since their parameters lie in accordance with the visible area.
PAGE 24
ROSTIV TECHNOLOGICAL INSTITUTE
SERVICE AND TOURISM
________________________________________________________________
Department of Radioelectronics
Lazarenko S.V.
LECTURE No. 1
from the discipline “Radio technical equipment and signals”
Rostov-on-Don
2010
lecture 1
ENTRY MAIN CHARACTERISTICS OF SIGNALS
Behind the discipline of RADIO TECHNICAL LANTZUGS AND SIGNALS
Hour: 2 years
Food, what to eat: 1. Subject, meta and course management
2. A short overview of the course, connections with other disciplines
3. A short history of the development of the discipline
4. The method of working on the course is inappropriate, you can take it,
forms of information, basic literature
5 Energy characteristics of the signal
6 Correlation characteristics of deterministic signals
7 Geometric methods of signal theory
8 Theory of orthogonal signals. Uzagalneniy row Fur'e
This lecture implements the following elements of qualification characteristics:
The student is required to know the basic laws, principles and methods of analyzing electrical circuits, as well as methods for modeling electrical circuits, circuits and devices.
The student is guilty of using the rules of the lantzugs in the established and transitional regimes.
1. SUBJECT 1 OF THE COURSE
The subject of the discipline is RADIO LANCEUGS and SIGNALS: electromagnetic processes in linear and non-linear radio-technical lancets, methods for the development of lancets in transient modes, the installation of continuous and discrete signals and their characteristics.
Type of discipline practice based on the subject of investigation - Typical lances and signals from physics - її laws of the electromagnetic field, from mathematics - tracking device.
The method of instilling discipline is to equip students with the basic understanding of the simplest radio engineering techniques and familiarize them with current algorithms for optimal signal processing.
As a result of the training in skin discipline, the student may
MOTHER OF THE APPEARANCE:
About daily algorithms for optimal signal processing;
About the trends in the development of the theory of radio engineering Lantzugs and signals,
NOBLE:
Classification of radio signals;
Timing and spectral characteristics of deterministic signals;
Vibration signals, their characteristics, correlation and spectral analysis of burst signals;
Discrete signals and their characteristics;
Algorithms for digital signal processing,
VMITI VIKORISTOVUVATI:
Methods of analytical and numerical solution of problems of passing signals through linear and nonlinear lancets;
Methods of spectral and correlation analysis of deterministic and fall signals,
VOLODITI:
Methods of changing the main parameters and characteristics of radio technical signals and signals;
Methods for analyzing the passage of signals through the Lancs,
MATI DOSVID:
Tracing the passage of deterministic signals through linear stationary lancets, nonlinear and parametric lancets;
The developments of the simplest radio-technical Lantzugs.
The operational directness of training from discipline is ensured by conducting laboratory workshops, at which time practical skills are imparted to every student:
Robots with electrical and radio devices;
Conducting an express analysis of current situations in robotic fragments of radio engineering Lancsugs following the results of extinctions.
2 A SHORT LOOK AT THE COURSE, A LINK TO OTHER DISCIPLINES
The discipline "Radiotechnical equipment and signals" is based on knowledge.і yah “Mathematics”, “Physics”, “Informatics”, it will ensure mastery of the art at scientists from advanced science and special disciplines, "Metrology and Radioism e Reniya", "Devices for generating and shaping radio signals", "Devices for receiving and processing signals", "Basics of television O technology", "Statistical theory of radio engineering systems", "Radio engineeringі Czech systems", coursework and diploma design to Tuvannya.
The discipline "Radiotechnical Lanyards and Signals" develops students' engineering skills, preparing them to master special disciplines.
The following disciplines are direct:
Students have thoroughly studied the basic laws, principles and methods of analyzing electrical cells, the physical essence of electromagnetic processes in radio electronics devices;
To cleave solid tips to analyze the installation and transition processes in lancets, as well as conduct experiments using the method of determining the characteristics and parameters of electric lancets.
The discipline consists of 5 sections:
1 Signals;
2 Passage of signals through linear lancets;
3 Nonlinear and parametric lancets;
4 Lantsugs with collar links and autocolivatal lantsugs
5 Principles of digital signal filtering
3. A BRIEF HISTORY OF THE DEVELOPMENT OF DISCIPLINE
The original theory of electrical and radio engineering is inextricably linked with practice: the development of electrical engineering, radio engineering and radio electronics. In the developments of significant areas, these theories have accumulated their contributions from numerous domestic and foreign studies.
The phenomena of electricity and magnetism have been known to people for a long time. However, in the other half of the eighteenth century, the stench began to grow seriously, and auras of secrecy and supernaturality began to appear from them.
Vzhe Mikhailo Vasilovich Lomonosov (1711 - 1765) Having conveyed that in nature there is only electricity and that electrical and magnetic components are organically interconnected with each other. A great contribution to the science of electricity was made by Russian academician France Epinus (1724 - 1802).
A turbulent development of knowledge about electromagnetic phenomena has become XIX centuries, driven by the intensive development of machine production. At this time, people are seeking for their practical needs TELEGRAPH, TELEPHONE, ELECTRICAL LIGHTING, METALS WELDING, ELECTRICAL MACHINE GENERATORS and ELECTRIC MOTORS.
Apparently, the chronological sequence of the most important stages in the development of knowledge about electromagnetism.
U 1785 Roci French physicist Pendant Charles Vidpovid (1736 - 1806) establishing the law of mechanical interaction of electric charges (Coulomb's law).
U 1819 Roci Danets Oersted Hans Christian (1777 - 1851) having revealed the action of the electric current on the magnetic needle, and in 1820 Roci French physicist Ampere Andre Marie (1775 - 1836) by installing a strong force (force) that acts from the side of the magnetic field onto the conductor section (Ampere’s law).
U 1827 Roci German physicist Ohm Georg Simon (1787 - 1854) having experimentally isolated the connection between tone and voltage for a piece of metal conductor (Ohm's law).
U 1831 Roci English physicist Faraday Michael (1791 - 1867) establishing the law of electromagnetic induction, and in 1832 Russian physicist Lentz Emilii Khristianovich (1804 - 1865) having formulated the principle of fluidity and turnover of electrical and magnetic boxes.
U 1873 based on the analysis of experimental data from electricity and magnetism, the English opinion of J. C. Maxwell proposed the hypothesis of the existence of electromagnetic coils and developed a theory for their description.
U 1888 Rotsi German physicist Hertz Heinrich Rudolf (1857 - 1894) experimentally achieved the development of electromagnetic coils.
Practical vikoristannya radiokhvil for the first time of the Russian teachings Oleksandr Stepanovich Popov(1859 - 1905), May 7, 1895 rock demonstrated at a meeting of the Russian Physico - chemical transmission (spark device) and reception of electromagnetic coils (lightning suppressor) .
For example XIX The century in Russia was celebrated by engineers and ever since Lodigin Oleksandr Mikolayovich (1847 - 1923), turning on the light to light the roasting lamp (1873); Yabluchkov Pavlo Mikolayovich (1847 - 1894), after unplugging the electric switch (1876); Dolivo-Dobrovolsky Mikhailo Osipovich (1861 - 1919), creating a triphasic system of strums (1889) And who fell asleep with daily energy.
At XIX Hundreds of years of analysis of electrical circuits have become one of the branches of electrical engineering. Electric lances were developed and insured according to physical laws that describe their behavior under the influx of electrical charges, voltages and streams. These physical laws became the basis for the theory of electrical and radiotechnical Lancsugs.
U 1893 – 1894 Rocks of Ch.Steinmetz and A.Kennelly buv apologies for the so-called symbolic method, which initially began to be used for mechanical grinding in physics, and then transferred to electrical engineering, where complex quantities began to be vicorized for a formalized representation of the amplitude phase picture of sinusoidal motion.
Based on Hertz's work(1888), and then Pupina (1892) with resonance and adjustment RLC circuits that of knitted injection systems solved the problem of determining the transmitting characteristics of the Lanzugs.
U 1889 A. Kennelly's work was formally broken down - mathematical method of equivalent reconversion of electric coils.
In the other half XIX Centuries Maxwell and Helmholtz developed the methods of contour streams and node stresses (potentials), which formed the basis of matrix and topological methods for analyzing the late hour. Helmholtz’s introduction to the principle of superposition was especially important. In addition, we will look at many simple processes in the same language with the advanced algebraic understanding of these processes in a more complex electrical phenomenon in the same language. The method of superposition allowed theoretically to revive a great number of facts that were previously considered indifferent and susceptible to empirical consideration.
At the same time, the established theory of electrical and radio engineering Lantzug was introduced into 1899 fate of understanding the complex support of the electric lancet to the zminny strum
An important stage in the formation of the theory of electrical and radio-technical Lancsugs was the investigation of the frequency characteristics of Lancsugs. The first ideas are also directly related to Helmholtz, who used the principle of superposition and the method of harmonic analysis for analysis. having stagnated the expanded functions to the Fourth series.
For example XIX centuries, the concepts of T-and P-like Lancsugians were introduced (they became known as the “Chotiripoles”). Just recently the concept of electric filters became clear.
The foundation of the current theory of radio engineering and radio engineering was laid by our scientists M.B. Shuleikin, B.A. Vedensky, A.I. Berg, A.L. Mints, V.A. . Papalexi and a lot of others.
4 COGNAL METHOD OF WORK OVER THE COURSE, ACTIVITIES, VITALITY FORMS, BASIC LITERATURE
Discipline is learned through lectures, laboratory and practical exercises.
Lectures are one of the most important types of initial activities O to form the basis of theoretical knowledge. They provide systematized foundations of scientific knowledge and discipline, concentrate respect e We use the most complex and knotty foods, stimulate her active cognitive activity, and form more creative thoughts.
During lectures, the order of fundamentals will be ensuredі the first step of practical directness is beginning. The compilation of the material is related to military practice, specific objects of special equipment, such as the stagnation of electric lances.
Laboratory activities are aimed at teaching students the methods of ek h experimental and scientific research, acquire skills in scientific analysis and formalization of results, skills in laboratory work O ores, control and testing devices and processing equipment. x no one.
During the hour of preparation before laboratory work, students study independently or (for needs) at general consultations. Yu This theoretical material, the basic procedure for carrying out research, draw up research forms (compile the diagram of the laboratory setup, the necessary tables).
Experiment is the main part of laboratory work and reality.і There is every student independently from the laboratory to laboratory work. Before carrying out the experiment, it should be carried out before n trolling experience in the form of a fly, meta - verification of the pituitary O training of students to laboratory work. In this case, it is necessary to pay attention to the knowledge of theoretical material, the order of research, and the nature of the obtained results. When receiving the following information: before neatness of decoration, finishing with students using ESKD, preparationі What is the correctness of the necessary steps.
Practical exercises can be carried out using the method of picking up a new skill in the world e no history, virus outbreaks. The main thing is the rights before tic robot skin student. In a practical business, screw your butt A what an applied nature. Advancement in computer technology d The preparation is based on practical activities in the way of vykonannya rozrakhunki e for additional help in programming microcalculators or personal EOMs. On the beginning of the skin lesion, a control test is carried out, meta kit O first - checking the preparedness of students before class, and also - activation A this is their cognitive activity.
In the process of acquiring discipline in students of the systemі Methodical skills and skills of independent work are being carefully formed. Students are reminded to properly supply food, supply food O in the simplest way, to convey the essence of the Vikonnoy robot, to make use of h some and other companions.
To strengthen the initial skills of preparation and carrying out initial training, students are being recruited as laboratory assistants.
Before the most important areas of cognitive activation I The students' news appears to be a problem. For its implementation O There are problematic situations in the course in general, in addition to topics and in O We ask what will be implemented:
To help introduce new problems, understand by showing how historically the stinks appeared and how the stinks stagnated;
Shlyakhom zіknennaya student with protirichchi between new phenomena e nyami and old understandings;
Due to the need to select the necessary information;
Vikoristannym rub between obvious knowledge of the e the results of decisions and the results of practice;
Presentation of facts and manifestations that are unreasonable at first glance
I will help with known laws;
The way to identify intersubject connections and connections between components.
In the process of learning discipline, control of mastered material on all practical types is assigned to the form of a flyer, and for topics 1 and 2, a form of double control work.
To achieve the best results, overall discipline requires T She's sleeping. Students who have completed all the basic programs and learned about all laboratory work are allowed to take the exam. V no positive assessments on the course work. Sleeping is carried out in detail T This form with the necessary written explanations in the classroom (formulas, graphs, etc.). A student is required to spend no more than 30 minutes to prepare. To prepare for the test, students can choose O You are allowed by the head of the department of methodological and developmental materials e reali. Preparation before confirmation can be done in writing. The head of the department can release students from the current situation, as shown about T special knowledge of the results of in-line control, provided by it n ki "excellently".
Thus, the discipline "Radiotechnical Lancsugs and Signals" is I There is a system of concentrations and at the same time you can get more A Thorough knowledge that allows the radio engineer to freely navigate the most important aspects of the operation of special radio devices and systems.
MAIN BASIC LITERATURE:
1. BASKAKIV S.I. Radiotechnical lances and signals. 3rd view. M: Vishcha school, 2000.
DODATKOVA LITERATURE
2. BASKAKIV S.I. Radiotechnical lances and signals. Pos_bnik until the end of the day: Head. Handbook for radio engineering. specialist. Vishiv. - 2nd visit. M: Vishcha shk o la, 2002.
3. POPOV V.P. Fundamentals of Lanzug's theory. Navch. for universities - 3 types. M: Vishcha shk o la, 2000.
5 ENERGY CHARACTERISTICS OF THE SIGNAL
The main energy characteristics of the speech signal are:
1) Mitt tension, which is calculated as the square of the mite value of the signal
Yakshcho | tension or strum, then the tightness that can be seen on the support and 1 Ohm.
The mitt pressure is not additive, since the mitt force of the sum of signals is not equal to the sum of their mitt forces:
2) Energy at an hourly interval is expressed as the integral of the mitten pressure
3) The average tension at the interval is determined by the energy value of the signal for this interval, added to one hour
de.
If the task signal is at an unexpired hour interval, then the average tension is calculated as follows:
Information transmission systems are designed so that information is transmitted in fewer tasks with minimal signal energy and intensity.
The energy and strength of signals that are detected at a certain hour interval can be additive, since the signals at that hour interval are orthogonal. Let's look at two signals and their tasks at hourly intervals. The energy and intensity of the sum of these signals is expressed as follows:
, (1)
. (2)
Here, i, energy and intensity of first and second signals, mutual energy and mutual intensity of these signals (or energy and intensity of their interaction). How to think about it
then the signals at hourly intervals are called orthogonal, and express(1) and (2) become visible
The concept of orthogonality of signals is closely related to the value interval.
One hundred complex signals are also characterized by the concepts of mitt effort, energy and average effort. These values are used to enter the energy characteristics of the complex signal using active values.
1. Mitt's tension is indicated by the addition of a complex signalon complex-receiving signal
2. Signal energyat intervals of an hour after the designated date
3. Pressure on the signalat intervals it is indicated as
Two complex signals, set at an hourly interval, are orthogonal, since their mutual intensity (or energy) is equal to zero.
6 CORRELATION CHARACTERISTICS OF DETERMINISTIC SIGNALS
One of the most important time-hour characteristics of a signal is the autocorrelation function (ACF), which allows one to judge the level of connection (correlation) of the signal with its copy destroyed over the hour.
For a speech signal specified at hourly intervalsand bounded by energy, the correlation function is determined by the next expression:
, (3)
de - the value of the time-hour value of the signal.
For skin values, the autocorrelation function is expressed as a numerical value.
W (3) It follows that the ACF is a paired function of the time-hour function. Effective, replace it with (3) change to, discard
If the signal is similar to its undamaged copy, the function is greaterreaches the maximum value that corresponds to the additional energy of the signal
In this case, the function of all signals, except periodic ones, changes (not necessarily monotonically) and, when the signals are completely destroyed, by an amount that exceeds the triviality of the signal, it turns to zero.
The autocorrelation function of a periodic signal is itself a periodic function with this very period.
To assess the degree of similarity of two signals, the mutual correlation function (MCF) is calculated, which is determined by the expression
Here i | signals set at an unexpired hour intervalAnd they are filled with end energy.
The value does not change, since the signal is obscured in advance of the first signal.
The autocorrelation function is approximated by the VCF phase, if the signal however
To replace the function in the zagalnyy type, there is no pairing and you can reach a maximum of three people.
The value indicates the mutual energy of the signals and
7 GEOMETRICAL METHODS FOR SIGNAL THEORIES
With the greatest wealth of theoretical and applied knowledge in radio engineering, the following are available: 1) In any sense, you can talk about the magnitude of a signal, stating, for example, that one signal significantly outweighs another; 2) How can one objectively evaluate to what extent two dissimilar signals are “similar” to one another?
U XX V. a functional analysis was carried out a branch of mathematics that explains our intuitive perceptions about the geometric structure of space. It turned out that the ideas of functional analysis make it possible to create a string theory of signals, which is based on the concept of a signal as a vector in a specially designed unlimited space.
Linear range of signals. Let me go -No signals. The reason for the consolidation of these objects the presence of active authorities, hidden from all elements of the multiplicity.
The investigation of the power of signals that create such multiplicities becomes especially difficult if it is possible to express one element of a multiplier through other elements. It is commonly said that the absence of signals is endowed with a song structure. The choice of these and other structures may be dictated by physical conditions. So, as many as 100 electrical fires are known, the stench can accumulate and also multiply by a fairly large factor. This makes it possible for multiple signals to introduce the structure of linear space.
The absence of signals creates a speech linear space, as the following axioms are true:
1. The be-yak signal takes on no verbal meaning for be-yak.
2. For any and all, their sum is, and it also fits in. The operation of subsumption is commutative: and associative: .
3. For any signal and any speech number, a signal is assigned=.
4. Bezlich M revenge special zero element , such that for everyone.
Since mathematical models of signals acquire complex values, then, assuming in the axioms 3 Multiplying by a complex number comes to the concept of a complex linear space.
Introducing the structure of linear space from the first step to the geometric interpretation of signals. Elements of linear spaces are often called vectors, drawing on the analogy between the powers of these objects and primary trivial vectors.
The boundaries that are imposed by the axioms of linear space are even harsh. Far from being a multiplicity of signals, a linear expanse is revealed.
Concept of coordinate basis. As in the original trivial space, in the linear space of signals one can see a special subset that plays the role of coordinate axes.
To say that the totality of vectors (}, to lie, and linearly independent, because of jealousy
It is possible to reduce all numerical coefficients to zero in just one hour.
A system of linearly independent vectors creates a coordinate basis for linear space. Is it possible to lay out the current signal?
then numbers() є projections of the signal to the selected basis.
In the current signal theory, the number of basis vectors is inevitably large. Such linear spaces are called endlessly worldly. Naturally, the theory of these spaces cannot be included in the formal scheme of linear algebra, since the number of basis vectors is always unique.
Standardized linear space. Energy of the signal. In order to continue and deepen the geometrical interpretation of the theory of signals, it is necessary to introduce a new concept, which in its place corresponds to the supremacy of a vector. It is better to give a precise sense of the meaning of “the first signal is greater than the other”, and to indicate how much greater it is.
Dovzhin vector of mathematics is called its norm. The linear range of signals is normalized, since the skin vector is clearly assigned a number the norm of this vector, and the following axioms of the normed space are defined:
1. The norm is unknown, then.. The norm is the same and more so, as .
2. For any number, jealousy is fair.
3. Yakshto and two vectors , then the unevenness of the tricubitus is revealed: .
You can use different ways to maintain the signal standard. In radio engineering, it is most often believed that analogue speech signals are normal
(4)
(In two possible ways, the meaning of the root is chosen more positively). For complex signals the norm is
de* symbol of a complex value. The square of the norm is called the energy of the signal
This energy itself is seen in the resistor with support 1 Oh, there's tension on this pressure.
Determine the norm for the signal using an additional formula (4) entirely for the following reasons:
1. In radio engineering, the magnitude of a signal is often judged from the overall energetic effect, for example, the amount of heat that is seen in a resistor.
2. The energy norm appears to be “insensitive” until the signal shape changes, perhaps significantly, or that occurs at short intervals of an hour.
Linear standardization scope with the end value of the standard form (1.15) It is called a space function with a square that is integrated, and is briefly designated.
8 THEORY OF ORTHOGONAL SIGNALS. UZAGALNA RANGE FUR'E
Having introduced the structure of linear space into many signals, having defined the norm and metric, we are able to reduce the possibility of calculating such a characteristic as between two vectors. This allows us to formulate an important concept of the scalar addition of elements of linear space.
Scalar addition of signals. We guess that since the initial trivial space has two vectors i, then the square of the modulus of their sum
de - scalar addition of these vectors, which lie somewhere between them.
By analogy, let’s calculate the energy of the sum of two signals:
. (5)
In addition to the signals themselves, their energies are non-additive - the energy of the total signal is replaced by the so-called mutual energy
. (6)
Equivalent formulas(5) that (6), significant scalar addition of speech signals:
The scalar has power:
- , de - speech number;
The linear space with such a scalar creation, which is unique to the sense that it is capable of containing all the boundary points of any sequences of vectors from this space that converge, is called the speech Hilbertian space.
Cauchy's fundamental uneasiness is correct Bunyakovsky
If the signals acquire complex values, then the complex Hilbertian space can be determined by introducing a new scalar solid behind the formula
so what.
Orthogonal signals and straightened Fourier series. Two signals are called orthogonal because they are a scalar, and therefore their mutual energy is equal to zero:
Let's go Hilbert space of signals with terminal energy values. These signals are assigned to each hour, the end and the end. It is acceptable that this section is given an undefined system of functions, orthogonal to each other and as such are the same norms:
To say, what is the basis in the space of signals of tasks of orthonormalization.
Let's expand the additional signal to the row:
(7)
Podannya (7) is called the normalized Fourth series of the signal on the selected basis.
The coefficients of this series are determined in this way. Let's take a basic function with a sufficient number and multiply the offending parts of the equation by it (7) And then we integrate the results hour by hour:
. (8)
Important for the orthonormality of the basis on the right side of the equation (8) lose only a member with a number, then
The possibility of detecting signals from the appearance of hidden Fourie rows is a fact of great importance. Instead, in order to determine the functional significance of impersonal points, we are able to characterize these signals with a curative (or, seemingly, unbroken) system of coefficients defined in the Fourier series.
The energy of the signal, represented in the form of a Fourier series. Let's take a look at the current signal, the decomposition of the series according to the orthonormal base system:
And we can calculate its energy by substituting this series directly into the integral:
(9)
Since the basis system of functions is orthonormal, we have (9) Only members with numbers will be considered as zero. A miraculous result emerges:
The meaning of the formula is as follows: the energy of the signal is the sum of the energies of all components, including the formation of the formal Fourier series.
Senior computer scientist of the Department of Radioelectronics S. Lazarenko
Chapter 1 Elements of the fundamental theory of radio signals
The term “signal” is often used in scientific and technical literature, and in everyday life. Sometimes, without worrying about the strictness of terminology, we define concepts such as signal, notification, information. To be clear, since the word “signal” is similar to the Latin term “signum” - “sign”, it has a wide range of meanings.
Prote, proceeding to the systematic development of theoretical radio technology, traces the extent to which it is possible to clarify the local sense of the concept of “signal”. According to the accepted tradition, the signal is the process of changing the physical state of any object that serves for imagery, registration and transmission of information. In practical human activity, information is inextricably linked to the information contained in it.
The food that is based on the concepts of “knowledge” and “information” is even broader. It is an object of great respect for engineers, mathematicians, linguists, and philosophers. In the 1940s, K. Shannon completed the initial stage of development of deep scientific knowledge - information theory.
It should be said that the problems identified here, as a rule, go far beyond the boundaries of the course “Radiotechnical Lantzugs and Signals”. Therefore, this book does not contain a connection that lies between the physical appearance of the signal and the place of the one laid out in the new message. There is no longer any discussion about the value of the information contained in the information contained in the signal.
1.1. Classification of radio signals
When starting to study any new objects and manifestations, science will first attempt to carry out its first classification. Below this test, a hundred signals are created.
The main meta is the development of classification criteria, as well as what is very important for the further establishment of singing terminology.
Description of signals for additional mathematical models.
Signals from physical processes can be captured using various devices – electronic oscillographs, voltmeters, receivers. This empirical method has significant shortcomings. Phenomena that are guarded by the experimenter will always appear as private ones, one by one, to reduce this world of uncertainty, so as to judge their fundamental power, transmitting the results in the minds that have changed .
In order to generate signals from objects of theoretical investigation and development, one must indicate a method for their mathematical description or, in my modern science, create a mathematical model of the signal being traced.
A mathematical model of the signal can be, for example, a functional delay, the argument of which is the hour. As a rule, such mathematical models of signals are designated by symbols of the Latin alphabet s(t), u(t), f(t), etc.
The creation of the model (at the time of the physical signal) is the first stage in terms of the dose of systematic implantation of the core of the box. First of all, the mathematical model allows us to abstract from the specific nature of the signal. In radio engineering, the same mathematical model with equal success describes the flow, voltage, strength of the electromagnetic field, etc.
The real side of the abstract method, which is based on the concept of a mathematical model, lies in the fact that we are able to describe the power of signals that objectively appear as initially important. In this case, a large number of other rows of signs are ignored. For example, in the majority of cases, it is important to select the exact functional conditions that would be expected in electric shocks, which are avoided experimentally. Therefore, the investigator, taking into account the totality of information available to him, selects from the available arsenal of mathematical models of signals those that in a particular situation most briefly and in the simplest way describe the physical process. Well, choosing a model is a highly creative process.
The functions that describe signals can have both speech and complex meanings. This is why we often talk about speech and complex signals. A violation of this or that other principle is on the right of mathematical clarity.
Knowing the mathematical models of signals, it is possible to compare signals with each other, establish their identity and validity, and carry out classification.
Same-world and multi-world signals.
A typical signal for radio technology is the voltage at the pump, either a lance or a strut at the head.
Such a signal, which is described by one clock function, is usually called univariate. This book most often receives simultaneous signals. However, it is sometimes necessary to manually enter rich world or vector signals into view.
the creation of a number of simultaneous signals. The whole number N is called the dimension of such a signal (the terminology is based on linear algebra).
A rich signal is, for example, the voltage system on the clamps of a rich terminal.
It is significant that the rich signal means that the totality of simultaneous signals is ordered. Therefore, in the halal mode, signals with different orders of component directing are not equal to one another:
Rich signal patterns are especially clear in cases where the functioning of folding systems is analyzed using an additional EOM.
Determined and discontinuous signals.
Another principle of classification of radio signals is based on the possibility or impossibility of accurately transferring their mitigation values at any given time.
If the mathematical model of the signal allows such transfer, the signal is called deterministic. The methods of doing this can be different - a mathematical formula, a calculation algorithm, a formula, a verbal description.
There are no strictly apparent deterministic signals, as well as related deterministic processes. The inevitable interaction of the system with physical objects that can be sensed, the presence of chaotic thermal fluctuations and simply the lack of knowledge about the cob mill of the system - all it is difficult to discern real signals as a function of the hour .
In radio technology, erratic signals often manifest themselves as disturbances that interfere with the acquisition of information from the received signal. The problem of combating code violations, increasing the resistance to radio reception code violations is one of the central problems of radio engineering.
You may think that the concept of a “fall signal” is super clear. However, this is not the case. For example, the signal at the receiving output of a radio telescope, direct to the cosmic transmission core, contains chaotic oscillations that carry various types of information about a natural object.
Between deterministic and random signals there is no unbreakable cordon.
Quite often in minds, if the value of the code is significantly less than the value of the signal with a known form, a more simply deterministic model appears to be completely adequate to the task.
The methods of statistical radio engineering, developed in the last decade for the analysis of the power of episodic signals, may have a lot of specific features and are based on the mathematical apparatus of the theory of homovirality and the theory of episodic processes. Which stake will be devoted entirely to the lower sections of this book.
Pulse signals.
A very important class of signals for radio technology are pulses, such as vibrations, which usually occur between the end of the hour. In this case, video pulses (Fig. 1.1 a) and radio pulses (Fig. 1.1 b) are separated. The difference between these two main types of impulses is the same. If it is a video pulse, then it is a corresponding radio pulse (frequency and frequency). In this case, the function is called the same radio pulse, and the function is called its replacement.
Small 1.1. Pulse signals and their characteristics: a - video pulse; b - radio pulse; c - assignment of numerical parameters to the pulse
In technical applications, instead of a new mathematical model, which provides details of the fine structure of the impulse, it is often correlated with numerical parameters, which makes it easier to understand its form. Thus, for a video pulse close to the shape of a trapezoid (Fig. 1.1, c), it is customary to calculate its amplitude (height) A. From the clock parameters, indicate the strength of the pulse, the strength of the front and the strength of the edge
In radio technology, there are voltage pulses, the amplitudes of which range from microvolt frequencies to several kilovolts, and the amplitudes range from nanosecond frequencies.
Analogue, discrete and digital signals.
Let’s finish with a short look at the principles of classification of radio signals. Often the physical process that gives rise to a signal develops over time in such a way that the meaning of the signal can fade away. Whatever the moment. Signals of this class are usually called analog (continuous).
The term “analog signal” emphasizes that such a signal is “analogous”, closely similar to the physical process that produces it.
A single-dimensional analog signal is visually represented by its own graph (oscillogram), which can be continuous or with interruption points.
Initially, radio technology used signals of the on-off analogue type. Such signals made it possible to successfully communicate with complex technical equipment (radio communications, television, etc.). Analogue signals could simply be generated, received and processed using the tools available to you.
Highly dependent on radio-technical systems, the diversity of conditions made it difficult to discover new principles of their work. In a number of outputs, analog ones have been replaced by pulse systems, the operation of which is based on a number of discrete signals. The simplest mathematical model is a discrete signal - a numerically impersonal point - a whole number) on the hour axis, each of which has a different value assigned to the signal. As a rule, the sampling time of the skin signal is constant.
One of the differences between discrete signals and analog signals is the need to generate a signal continuously at all times. This makes it possible for one or the other radio line to transmit information from different devices, organizing a multi-channel connection with a number of channels per hour.
It is intuitively clear that analog signals, which change rapidly over time, require little time to sample them. Corner. 5 This fundamentally important nutrition will be examined in detail.
We distinguish a variety of discrete signals - digital signals. They are characterized by the fact that the reference values are represented in the form of numbers. In order to reduce the technical difficulties of implementation and processing, it is necessary to use double numbers with interchange and, as a rule, there is no need for a large number of digits. Recently, there has been a trend toward widespread adoption of systems using digital signals. This is due to significant advances achieved by microelectronics and integrated circuit technology.
Keep in mind that, in essence, any discrete or digital signal (we are talking about a signal is a physical process, not a mathematical model) or an analog signal. Thus, an analog signal that changes frequently over the course of an hour can be given a discrete image that looks like a sequence of straight-through video pulses of the same magnitude (Fig. 1.2, a); The height of these pulses is proportional to the values at the extreme points. However, it is possible to find it in another way, preserving the height of the stationary pulses, but changing their intensity to the exact same values (Fig. 1.2, b).
Small 1.2. Sampling of an analog signal: a – with a changing amplitude; b - with variable trivality of the neuronal impulses
The two methods presented here for sampling an analog signal become equivalent, since the value of the analog signal at the sampling points is proportional to the area of the surrounding video pulses.
Fixing the different values in the view of numbers is done by displaying the remaining sequences of video pulses in the view. The double number system is ideally suited for this procedure. You can, for example, set one to high and zero to low level of potential, f Discrete signals and their power are detailed in detail. 15.
2.1.1.Determined and sporadic signals
Determinative signal– this signal, the mitteve value of which at any time can be transmitted with equal accuracy.
The application of a deterministic signal (Fig. 10) can be: sequences of pulses (shape, amplitude and position in certain modes), continuous signals from specified amplitude-phase relationships.
Methods for determining the MM signal: analytical expression (formula), oscillogram, spectral manifestation.
The butt of the MM signal is deterministic.
s(t)=S m ·Sin(w 0 t+j 0)
Vipadkovy signal– a signal whose significance is unknown at any time, and can be transmitted with some confidence, less than one.
With the butt of a voltage signal (Fig. 11) there can be a voltage, which corresponds to human thought and music; sequence of radio pulses at the input of the radar receiver; make some noise.
2.1.2. Signals that can be detected in radioelectronics
Uninterrupted by value (level) and uninterrupted by hour (uninterrupted or analogue) signals– take any values s(t) and find them at any moment at a given hour interval (Fig. 12).
Continuous signals based on magnitude and discrete signals depending on the hour given at discrete values of the hour (at a multiple of points), the value of the signal s(t) at these points takes on the same value at the same interval along the ordinate axis.
The term “discrete” characterizes the method of assigning a signal to the hour axis (Fig. 13).
Quantized by magnitude and continuous signals by hour tasks on the entire clock axis, otherwise the value of s(t) can be filled with discrete (quantized) values (Fig. 14).
Quantized by value and discretely by hour (digital) signals– values equal to the signal in the digital form are transmitted (Fig. 15).
2.1.3. Pulse signals
Impulse- Kolivannya, which only sleeps between the end of the hour. In Fig. 16 and 17 show the video pulse and radio pulse.
For trapezoidal video pulse, enter parameters:
A – amplitude;
t i – severity of the video pulse;
t f – triviality to the front;
t sr - soreness immediately.
S р (t) = S (t) Sin (w 0 t + j 0)
S in (t) - video pulse - a signal for radio pulse.
Sin(w 0 t+j 0) – completion of the radio pulse.
2.1.4. Special signals
On function (one by one function(Fig. 18) or Heaviside function) describes the process of transition of any physical object from the “zero” to the “single” state, and this transition is facilitated by mittevo.
Delta function (Diraku function) This is an impulse, the value of which is zero, and the height of the impulse inevitably increases. It is customary to say that the function is concentrated at this point.
 | (2) |
| (3) |
First of all, before studying any phenomena, processes or objects, the science will first attempt to classify them according to the greatest degree possible. A similar test of completely radio-technical signals and code conversion is acceptable.
The basic concepts, terms and definitions of the standard for radio-technical signals are established by the national standard “Radio-technical signals. The terms are meaningful." Radio technical signals are even different. They can be classified at a low level.
1. Radio technical signals can be manually viewed using mathematical functions specified in physical coordinates. From what point of view the signals are divided into same-worldі rich world. In fact, simultaneous signals have the greatest width. The stench sounds with the functions of the hour. Multi-dimensional signals are formed from the absence of simultaneous signals, and in addition, reflect their position n- peaceful space. For example, signals that carry information about the image of any object, nature, people or creatures, and the functions of that time and position on the surface.
2. Due to the peculiarities of the structure of the time-hour data, all radio signals are divided into analog, discretelyі digital. Lecture No. 1 has already looked at their main features and functions, one after another.
3. Beyond the stage of visibility of a priori information, all varieties of radio signals are usually divided into two main groups: determined(regular) and vipadkovi signal. Determinatives are radio engineering signals whose meanings are reliably known at any time. The application of a deterministic radio-technical signal can be a harmonic (sinusoidal) waveform, sequence or packet of impulses, shape, amplitude and time-clock position of which are visible from afar. In essence, the deterministic signal does not carry any information and almost all of its parameters can be transmitted over the radio communication channel with one or more code values. In other words, deterministic signals (messages) essentially do not contain information, and there is no sense of their transmission. You are welcome to use the software to test communication systems, radio channels and other devices.
Deterministic signals are divided into periodicallyі non-periodic (impulse). The pulse signal is a signal of end energy, clearly visible from zero during the interval of an hour, equal to the hour of completion of the transition process in the system, which is the signal of significance. Periodic signals occur harmonious, so as to remove one more harmonic, and polyharmonic The spectrum of which is formed from the impersonality of harmonious warehouses. The harmonic signals are preceded by signals that can be described by the sine or cosine function. The solutions of all signals are called polyharmonic.
Vipadkov signals- These signals, whose meanings are unknown at any time, cannot be transmitted with the same reliability as traditional units. As paradoxical as it may seem at first glance, a signal that carries useful information may be an odd signal. The information is embedded in the absence of amplitude, frequency (phase) or code changes in the signal that is transmitted. In practice, any radio-technical signal that contains valuable information can be considered as faulty.
4. In the process of transmitting information, signals may be subject to other transformations. This is due to that name: signals modular, demodulated(detected), coded (decoded), strengthened, blurred, discretized, quantized ta in.
5. Based on the meanings of signals generated during the modulation process, they can be divided into modulating(the first signal that is modulated by constant vibration) or modular(Nesuche kolyvannya).
6. In relation to other types of information transmission systems, they are separated telephone, telegraph, radio stations, television, radar, caring, vimirivalnye and other signals.
Let's now look at the classification of radio engineering codes. Pid radio engineering conversion understand the fallout signal, similar to the red one and occurring at the same time as it. For radio communication systems, the transcode is not a kind of surge on the red signal, which reduces the accuracy of the information that is being transmitted. Classification of radiotechnical cross-codes is also possible based on low values.
1. After a month of guilt, divide by externalі internal. The main types have already been discussed in lecture No. 1.
2. It is important to separate the nature of the interaction between the signal and the signal additiveі multiplicative pereshkodi. A transcode that is implied by a signal is called additive. A transcode is called multiplicative because it is multiplied by a signal. In real channels, the connection is due to place and additive and multiplicative transitions.
3. Based on the main powers of additive transfers, they can be divided into three classes: focus on the spectrum(Vuzkosmugovi pereshkodi), Impulse interruptions(average in hours) and fluctuations(fluctuation noise), not separated by either an hour or a spectrum. Spectrum-neutral ones are called transients, most of which are located in close areas of the frequency range that is less than the transmission of the radio engineering system. A pulse transient is a regular or chaotic sequence of pulse signals similar to the red signal. The cores of such transitions are digital and switching elements of radio-technical devices or devices that operate alongside them. Impulse and cyclic disturbances are often called guidance.
There is an important difference between the signal and the speed of the day. Moreover, there is a stench in the food, even if you care about your life.