Antipyretic remedies for children are prescribed by a pediatrician. But there are situations of indispensable help for fevers, if the child needs to give faces negligently. Then the fathers take on themselves the resuscitation and stop the antipyretic preparations. What can be given to infants? How can you lower the temperature in older children? What are the most safe faces?
The first thing to do is to start developing some new phenomena, processes of chi objects, and science should start to carry out their classification for possibly greater signs. To see and analyze the signals, we can see their main classes. This is necessary for two reasons. First, reverification of the validity of a signal to a specific class is an analysis procedure. In another way, in order to present and analyze the signals of different classes, it is often necessary to win over different results and approaches. The main concepts, terms and definitions in the gallery of radio engineering signals are establishing the national (earlier sovereign) standard “Radio engineering signals. Terms and definitions. "Radio engineering signals are supra-signally different. A part of the short classification of signals for a low sign is shown in Fig. 1. Reporting about the series was made farther away. signal gap is described by one (one-dimensional signal; n = 1), two
(two-world signal; n = 2) or more (multiple signal n > 2) independent changes. One-way signals with functions for more than an hour, and different ones, moreover, reflect the position in the n-world space.
Fig.1. Classification of radio engineering signals
It will be for the sake of simplicity that, in the main, it is possible to look at one-dimensional signals that lie late at the hour, the material of the initial helper is allowed to be aggravated and to a rich variety, if the signal is presented at the end of the day, or at an unswallowed sukupnosti point, put, I live. In TV systems, the signal of a black-and-white image can be seen as a function f(x, y, f) of two space coordinates and time, which represents the intensity of vibration at point (x, y) at time t on the cathode. When transmitting a color television signal, there can be three functions f(x, y, t), g(x, y, t), h(x, y, t), assigned to a trivi- mer multiplier ). fields). In addition, different views of television signals can be blamed for the hour of transmission of a television image with sound.
Rich signal - the sequence of one-dimensional signals is ordered. A rich signal is created, for example, by a system of tension on the folds of a rich polypole (Fig. 2). Rich signals are described by collapsible functions, and now processing is often possible in digital form. Therefore, rich models of signals are especially different in different situations, if the functioning of folding systems is analyzed with help of computers. Also, rich, or vector, signals are added up from anonymous one-dimensional signals
where n is the whole number, the size of the signal.
R 
ic. 2. The system of springs of the bagatopole
Due to the peculiarities of the timing data structure (Fig. 3), all radio technical signals are subdivided into analog (analog), discrete (discrete-time; in Latin discretus - divisions, divisions) and digital (digital).
If the physical process, which generates a one-dimensional signal, can be detected by an uninterrupted function for the hour u(t) (Fig. 3, a), then such a signal is called analog (uninterrupted), otherwise, it is narrowed, continuous , explore along the amplitude axis It is important to note that the term “analogue” is vibrated from the description of the signals, which are uninterrupted at the hour. An uninterrupted signal can be interpreted as a real or complex signal at the hour u(t), which is a function of an uninterrupted actional timchasovoy change. The concept of an "analog" signal is related to it, that whether it be a mittve, the value is similar to the law of change of a viable physical quantity in an hour. butt analog signalє deak voltage, as filed at the input of the oscilloscope, as a result of which on the screen there is an uninterrupted curve as a function of the hour. The shards of modern processing of uninterrupted signals with variable resistors, capacitors, operational inputs can hardly be used with analog computers, the term "analog" is not seen very well these days. More correctly, it would be called a non-stop signal processing, those that today sound are called analog signal processing.
In radioelectronics and technology, communication is widely used in pulse systems, attachments and lances, which are based on various discrete signals. For example, an electric signal, which reflects the language, is uninterrupted like for a equal, so for an hour, and the temperature sensor, which can see the value through the skin 10 times, serve as a dzherel of uninterrupted signals for values, but discrete for an hour.
The discrete signal has a special analog path. The process of converting an analog signal into a sequence of responses is called sampling, and the result of such a conversion is called a discrete signal or a discrete series.
The simplest mathematical model of a discrete signal 
- sequence of points on the clock axis, taken, as a rule, through equal intervals of the hour 
, Named by the sampling period (or interval, sampling time; Sample time), and in the skin of any task, the value of an uninterrupted signal (Fig. 3, b). The value wrapped up to the sampling period is called the sampling frequency: 
(otherwise known 
). Vidpovidna їy kutova (circular) frequency is displayed as follows: 
.
Discrete signals can be created without intermediary dzherel _information (zocrema, discrete signals from sensors in keruvannya systems). The simplest butt of discrete signals can be reports about the temperature, which are transmitted in the news programs of radio and television broadcasts, and in the pauses between such transmissions of reports about the weather, they do not sound. It is not necessary to think that discrete alerts can be converted to discrete signals, and non-stop alerts - non-stop signals. Most often, the most uninterrupted signals are the transmissions of discrete accompaniments (as carriers, i.e. carriers). Discrete signals can be rewired for transmission without interruption.
It is obvious that in the wildest way of giving a non-stop signal by a set of discrete signals to lead to a simple loss of core information, we don’t know anything about the behavior of the signal in the intervals between the signals. However, it uses a class of analog signals, for which such information is practically not used, and therefore the stench can be with a high degree of accuracy of observation of the values of their discrete signals.
A variety of discrete signals is a digital signal. 
. With this value, the equal signal can be numbered with two numbers with the final number of discharges, necessary. A signal that is discrete at the hour of quantizations is called a digital signal. Before speech, signals, quantized after equal, but without interruption at the hour, are rarely practical. A digital signal has a discrete value for the signal 
the scale is quantized by equals (Fig. 3, c) and then the quantization of the discrete signal is replaced by numbers 
most often implemented in a double code, which is high (one) and low (zero) equal voltage potentials - short pulses of trivality 
(Fig. 3, d). Such a code is called unipolar. Oscilki vidlіki can nabuvaty kіntseve impersonal value of equal voltage (divided by another indicator in Fig. 3, d, which in digital looks practically equally movingly can be recorded both with the number 5 - 0101, and with the number 4 - 0100), then when a signal is given, it is inevitable yogo rounding off. Rounding pardons, which are blamed for cioma, are called pardons (or noises) of quantization (quantization error, quantization noise).
The sequence of numbers, which represents the signal for the hour of digital processing, is a discrete series. The numbers that make the sequence, the values of the signal in the range (discrete) moment and hour, are called digital signal samples (samples). The given quantized value signal is given to a visual set of pulses, which characterize zeros (“0”) and ones (“1”) when a value is given in a binary number system (Fig. 3, d). Gaining pulses of victors for amplitude modulation of a carrier-like colivanna and otrimannya code-impulse radio signal.
As a result digital processing nothing “physical” should come out, only numbers. And the numbers are an abstraction, a way to describe information that can be avenged from an acquaintance. Otzhe, we need to mother schos physical, scho representable numbers or wear numbers. Also, the essence of digital processing lies in the fact that a physical signal (voltage, strum, etc.) is transformed into a sequence of numbers, as if it were mathematical transformations in a numerical extension.
Transformation of a digital signal (sequence of numbers) for the need to change back, at the voltage or strum.
Digital processing of signals is given a wide range of possibilities for transferring, accepting that transformation of information, including those that cannot be implemented with the help of analog technology. In practice, the analysis and processing of signals, in most cases, digital signals, are replaced by discrete ones, as the understanding of digital signals is interpreted as quantization noise. At the link with the cim of the effect, related to the quantization of the equal and digitized signals, the majority of the fluctuations are not taken to respect. It can be safely said that in discrete and digital channels (zocrema, in digital filters) discrete signals are processed, but in the middle of the structure of digital channels, signals are represented by numbers.
The number of attachments used for signal processing can operate with digital signals. It is also based on an extension, based on analog circuitry, as it is used with discrete signals, representing pulses of different amplitudes, trivality or repetition frequency.
One of the main signs, how the signals are distinguished, is the transmission of the signal (its value) at the hour.
R 
ic. 3. Radio engineering signals:
a - analog; b - discrete; c - quantizations; g - digital
According to mathematical manifestations (for the level of a priori manifestation, in lat. a priori - from the front, i.e., additional information), all radio engineering signals are divided into two main groups: determinants (regular; determined) and signals (casual) 4).
Determinants are called radio engineering signals, mittev the meaning of such whether or not the hour is trustworthy, so that they are transferred to the imovirnistyu, which are healthy alone. Deterministic signals are described in advance by given functions to the hour. Before speech, mittve the meaning of the signal - the whole world of that, like the meaning and in the way it directly changes from zero; In this way, the meanings of the signal can be both positive and negative (Fig. 4, a). The simplest butts of a deterministic signal are harmonization with a visible cob phase, high-frequency oscillations, modulation according to a given law, a sequence or a burst of impulses, a shape, an amplitude and a timing position in advance.
Yakbi podomlennya, scho transmitted through the channels zv'yazku, was determined, so far ahead of us with full reliability, then yogo transmission would be stupid. Such determinated information should not be avenged by any new information. To that, let’s look at it like a vipadkovі podії (or vipadkovі functions, vipadkovі value). Otherwise, it seems that there may be a few options for explaining (for example, an impersonal difference in pressure, which can be seen by the sensor), for which they are implemented with a simple imovirnistyu alone. At the link with the cym the signal is a vypadkovy function. Determination signal can be carried information. Yogo can be tested only for testing the radio-technical transmission system, or testing about okremih її outbuildings. The vipadkovy character is reconsidered, and to induce a shift in the zoom, having the most important meaning of the theory of immorality in the prompt theory of transmission.
Mal. 4. Signal:
a - determinations; b - vipadkovy 
Deterministic signals are subdivided into periodic and non-periodic (impulses). The signal of the end energy, initially in the form of zero, with a short interval of an hour, equal to the hour of the completion of the transitional process in the system, for the sake of assignments, is called an impulse signal.
Signals are called vipadkovymi, mittєvі znachennya such at any moment you don’t know and can’t be transferred to the mood, which is good alone. In fact, for vipadical signals, one can know only the imovirnіst of that, which in the future will be of any significance.
You can give up, but the understanding of the “vipadic signal” is not known correctly.
But not so. For example, the voltage at the output of a thermal imager, which is directly connected to the IR-vibration, represents a chaotic oscillation that carries different information about the object that is being analyzed. Strictly seeming, all the signals that sound in practice are vague and most of them represent chaotic functions of the hour (Fig. 4, b). It is not paradoxical at first sight, but a signal that carries basic information, may be more than a vipadkovy signal. The information in such a signal is embedded in the impersonal amplitude, frequency (phase) or code changes of the signal that is being transmitted. Signals zv'yazku at the hour change the mitte of the value, moreover, the changes can be transferred only with the action of a smaller one. In this order, signals the connection to the singing world by the vypadkovyh processes, that and їх are described by additional methods, similar to the methods of describing the vypadkovyh processes.
In the process of transmitting core information, radio engineering signals can be supported by another transformation. Tse sound in their names: signals of modulation, demodulation (detection), encoded (decoded), enhanced, truncated, sampled, quantized and other.
For recognition, as signals may be in the process of modulation, they can be divided into modular (the first signal, which modulates without any coercion) or modulation (not columation).
For belonging to another type of radio engineering systems, systems for transmitting information, distributing “sounds”, telephone, telegraph, radio, television, radiolocation, radionavigation, vimiryuvalnі, keruyuchі, services (at .
A short classification of radio technical signals has been introduced, which does not overwhelm their diversity.
Chapter 1
The term "signal" is often used in science and technology nutrition, and in everyday life. Sometimes, without thinking about the strictness of the terminology, we note that it is understandable, like a signal, reminder, information. Sounds like the word “signal” sounds like the Latin term “signum” - “sign”, there is a wide range of meanings.
Prote, proceeding to a systematic development of theoretical radio engineering, the next step is to clarify the change of the sense of understanding the "signal". Apparently, to the accepted tradition, a signal is called the process of change at the hour of the physical state of any object that serves for display, registration and transmission of awareness. In practice, human activities are inconsistently connected with the information laid down in them.
Kolo nutrition, which is based on the concepts of "information" and "information", is even wider. Wine is an object of sawing respect for engineers, mathematicians, linguists, philosophers. In the 1940s, K. Shannon completed the first stage of the development of deep scientific directly - the theory of information.
Needless to say, the problems here, as a rule, go far beyond the course of "Radio engineering lances and signals." That is why in this book there is no link, which is a physical signal that looks like a signal that is laid out in a different way. Tim no longer talk about the value of information, laid down in the instructions, allowed, in the signal.
1.1. Classification of radio engineering signals
Proceeding to the discovery of whether there are any new objects of existence, science has to start planning to carry out their first classification. Below, such a test is given a hundred signals.
The main meta - variation of the criteria for classification, and also, which is even more important for the distant introduction of singing terminology.
Description of signals for additional mathematical models.
Signals as a physical process can be connected with additional accessories and attachments - electronic oscillographs, voltmeters, priymachiv. Such an empirical method may be of little value. Phenomena, which are guarded by the experimenter, always appear as private, show one by one, relieve this world of confusion, as if judging about their fundamental power, transmit the results in the minds that have changed.
In order to generate signals with the objects of theoretical development and rozrachunkiv, it is necessary to indicate the method of their mathematical description, or, apparently by modern science, to create a mathematical model of the received signal.
A mathematical model of a signal can, for example, have a functional staleness, the argument of which is an hour. As a rule, such mathematical models of signals are given by the symbols of the Latin alphabet s(t), u(t), f(t), etc.
The creation of the model (in this way physical signal) - the first suttviy krok on the path of systematic cultivation of the quality of the appearance. Nasampered mathematical model allows abstraction from the specific nature of the signal. In radio engineering, that mathematical model itself describes the strum, voltage, and intensity of the electromagnetic field with equal success.
The essence of the abstract method, which is based on understanding mathematical models, I believe in what we take to be able to describe the very power of the signals, as if they act objectively as if they were originally important. When this is ignored, there is a large number of other row signs. For example, in the case of more important vipadkіv, it is important to choose the exact functional fallows, yakі podvіdali b elektrichnymi kolvannyam, scho poserіgayutsya experimentally. Therefore, the reporter, looking at all the variety of information available to you, chooses from the obvious arsenal of mathematical models of signals, which, in a particular situation, describe the physical process in the best and simplest way. Otzhe, choosing a model is a creative process of a meaningful world.
Functions that describe signals can take on both verbal and complex meanings. To that nadali often speaks about speech and complex signals. Vykoristannya that chi іnshoy principle - on the right mathematical zruchnostі.
Knowing the mathematical models of signals, you can compare signals among themselves, establish their identity and identity, and classify them.
Single and different signals.
A typical signal for radio engineering is the voltage on the zatiskachi of any kind of lancer or strum at the neck.
Such a signal, which is described by one function of the hour, is usually called the same. In this book, the same-world signals are most often seen. However, sometimes you can manually introduce rich visuals, or vector signals to the mind.
approved by the deakim of the impersonal signals of the same world. In general, the number N is called the size of such a signal (the terminology is taken from linear algebra).
For example, the system of tension on the clasps of the bagatopole is to serve as a bagatomire signal.
Significantly, scho rich signal - the sequence of one-dimensional signals is ordered. To that, in a wild manner, signals with a different order of directing the components are not equal to one to one:
Bagomirn models of signals are especially correct in case of folding systems, if the functioning of folding systems is analyzed with the help of EOM.
Determination and vipadkovy signals.
The second principle of classification of radio engineering signals is based on the possibility or impossibility of an accurate transfer of their mittiev values at any given moment.
Since the mathematical model allows the signal to be transferred in such a way, the signal is called deterministic. Ways of yoga task can be different. mathematical formula, calculation algorithm, nareshti, verbal description.
Strictly seeming, deterministic signals, like and vidpovidnyh їm deterministic processes, no. Inevitably, the interaction of the system with physical objects, which will make you feel strange, the presence of chaotic thermal fluctuations and simply the lack of knowledge about the cob mill of the system - it’s all worth looking at the real signals like a fluctuation of the function of the hour.
In radio engineering, vipadkovy signals often manifest themselves as a shift, which shifts the received information from the received call. The problem of combating overshifts, increasing the stability to the overshift of radio reception is one of the central problems of radio engineering.
You can figure out how to understand the “vipadic signal” is super clear. However, it is not so. For example, the signal at the output of the receiver of a radio telescope, directed to the dzherelo cosmic vibration, is a chaotic coli, which carries, prote, various information about a natural object.
Between the determinants and vipadkovy signals there is no non-searchable cordon.
Even more often in the minds, if the value of the shift is significantly less than the value of the coris signal with the given form, the more simply determined model appears as a whole adequate to the task.
Statistical radio engineering methods, which have been used for the last ten years for power analysis fluctuation signals, may have a lot of specific figs and are based on the mathematical apparatus of the theory of dynamics and the theory of vibrational processes. Which number of food will be dedicated again to the low distribution of the book.
Pulse signals.
Even more important for radio engineering is the class of signals and impulses, so that the ringing, which is only used in the midst of the end of the hour. At the same time, video pulses (Fig. 1.1 a) and radio pulses (Fig. 1.1 b) are separated. Vіdminnіst mіzh tsimi two main types of impulses y axis y chomu. If it is a video pulse, then it is a viable radio pulse (the frequency is quite enough). With which function is called the outgoing radio pulse, and the function is called the second command.
Mal. 1.1. Impulse signals and their characteristics: a - video impulse; b - radio pulse; c - assignment of numerical parameters per impulse
In technical studies, the replacement of a new mathematical model, like the main details of the fine structure of the impulse, is often corroded by numerical parameters, which makes it easier to understand the form. So, for a video pulse that is close to the shape of a trapezoid (Fig. 1.1, c), it is customary to assign an amplitude (height) А.
In radio engineering, there are voltage pulses on the right, the amplitudes of which lie at the borders of the microvolt frequency up to a few kilovolts, and the trivality reaches the frequency of a nanosecond.
Analogue, discrete and digital signals.
Concluding a short review of the principles of classification of radio engineering signals, it is significant. Often the physical process that generates the signal develops in such a way that the signal's meaning can be undermined. be like a moment of time. Signals of this class are usually called analog (continuous).
The term "analogue signal" substantiates that such a signal is "analogue", similar to the physical process that it generates.
A single-mode analog signal is initially represented by its own graph (oscillogram), which can be uninterrupted, as well as with points of expansion.
At the same time, radio engineering vikoristovuvalis signals of the switch-to-analog type. Such signals made it possible to successfully vibrate visually incoherently. technical tasks(Radio communication, television broadcasting, etc.). Analogue signals were simply generated, accepted and processed for additional assistance available to the roki.
Growth was able to reach radio engineering systems, versatility of zastosuvan zmusili shukati new principles їх obudovi. The analogous ones in a number of modes were replaced by impulse systems, the operation of which is based on different discrete signals. The simplest mathematical model of a discrete signal is the numberless numberless point - the integer number) on the axis of the hour, for the skin of which the value of the signal is assigned. As a rule, the rate of discretization of the skin signal is constant.
One of the advantages of discrete signals in comparison with analog ones is the fact that it is necessary to check the signal without interruption at all times. For rahunok z'yavlyaєtsya mozhlivіst odnієї i tієї zh radiolіnії transmit podomlennya vіd raznyh dzherel, arranging rich-channel zv'yazok z podіlom kanalіv per hour.
It is intuitively clear that analog signals, which change rapidly in hours, require a small amount of time for their sampling. Injection. 5 tsey fundamentally important food will be followed up in detail.
Let's specialize in a variety of discrete signals - digital signals. It is characteristic of those that the reference values are presented in visual numbers. From the mirkuvan tekhnіchnіh zruchnosti realіzіzії and obrobki zvіkorovuyut dvіykovіt dvіykovі number z zamezhenіm і, as a rule, not a great number of ranks. In the rest of the hour, there was a trend of wide deployment of systems with digital signals. This is due to the significant success achieved by microelectronics and integrated circuitry.
Slid mother on uvazі, scho in fact be a discrete or digital signal (mova go about the signal - a physical process, and not about a mathematical model) - an analog signal. So, an analog signal, which changes regularly in hours, can be given a discrete image, which can look like a sequence of rectilinear video pulses of the same trivality (Fig. 1.2, a); the height of the ethnic impulses is proportional to the values at the vіdlіkovy points. However, you can go in a different direction, saving the height of the pulses in the constant, but also changing the trivality of the current to the current values (Fig. 1.2, b).
Mal. 1.2. Discretization of the analog signal: a - with a change in amplitude; b - with a change in the trivality of the wave impulses
The offense presented here is the sampling method of the analog signal becoming equivalent, assuming that the value of the analog signal at the sampling points is proportional to the square of the other video pulses.
Fixing the significant values of the visual numbers is influenced by the path of the remaining ones in the visual sequence of video impulses. Double numbering system is ideal for this procedure. It is possible, for example, to set one to a high, and to zero - a low equal to the potential, f Discrete signals and their power are detailed in the goal. 15.
Basic radio engineering processes
Changeover of the external alarm to the electric signal.
Generation of high-frequency waves.
Control of colivation (modulation).
Posilennya weak signals at the adoptive
Vidіlennya povіdomlennya z high-frequency noise (detektuvannya and dekoduvannya).
Radio engineering lancers and methods
their analysis
Classification of lanceugs
І elements, which are victorious for the creation of re-arranged signal transformations and colivans, can be divided into the following main classes:
Linear Lanziugs permanent parameters;
Linear lancets with changing parameters;
Non-linear lancers.
^
Linear lancets with constant parameters
You can use the following definitions:
Lantsyug is linear, as it is the elements that enter before the new, do not lie in the presence of a strong force (voltage, struma), that is on the lantsyug.
Linear lancet follows the principle of superposition (overlay).
De L is an operator that characterizes the influx of the lancer on the input signal.
When acting on a linear lance, a number of external forces, the behavior of a lance (strum, tension) can be determined by a way of overlay (superposition) solution, known for skin forces okremo.
Otherwise: in a linear lance, the sum of effects in the case of the same infusions is greater than the effect in the sum of the infusions.
Be-yakoy collapsible dії in a linear lance with constant parameters do not blame the splitting of new frequencies.
^ Linear lancets with changing parameters
The lancers are toiling in the air, one or more of the parameters of which change in the hour (but do not lie down at the input signal). Similar lancers are often called linear. parametric.
Power 1 and 2 of the preceding paragraph are valid for tsikh kіl. However, I create the simplest harmonic infusion in a linear lance with changing parameters of folding, which makes the frequency spectrum.
^ Non-linear lancers
Radiotechnical language is non-linear, so that only one or a few elements enter the warehouse, the parameters of which are equal to the input signal. The simplest non-linear element is a diode.
Main Powers non-linear languages:
To non-linear lances (i elements) the principle of superposition does not stop.
The important power of the non-linear stake is the transformation of the signal spectrum.
^ Signal classification
From the informational point of view, the signal can be subdivided into determinations and trends.
Determinate naming a be-a-signal, a mittve of the meaning of a be-a-be-a-mite hour can be transferred from an imovirnistyu loneliness.
Before vipadkovim send signals, mittev the meanings of which are not far away, and can be transferred only with some kind of imovirnistyu less than one.
In theory and practice, the order of the blue vipadical signals is brought to the mother on the right with vipadical shifts - noises. Corresponding vipadkovі signals, as well as reshuffles often use the term vipadkovі kolyvannya or vipadkovі processes.
Signals in the radio communication channel are often subdued to important signals and on radio signals; under the first ones, they are modular, and under the others, modulation is done.
Signals that are stagnant in modern radio electronics can be divided into the following classes:
Dovіlnі for the value of that without interruption for an hour (analogue);
Dovіlnі for the value of that discrete per hour (discrete);
Quantization by magnitude and without interruption by the hour (quantization);
Quantization by value and discrete by hour (digital).
^
Characteristics of determinations
signals
Energy characteristics
The main energy characteristics of the speech signal s(t) are the intensity and energy.
Mitteva's tension shows up like a square mitte meaning s(t):
The energy of the signal on the interval t 2 t 1 is shown as an integral of the mitt pressure:
.
Setting
Average sensing interval t 2 , t 1 signal tightness.
^
Giving a good signal
at the sight of sumi elementary colivans
For the theory of signals and their processing, the value of the distribution of the given function f(x) from different orthogonal systems of functions j n (x) is important. If there is a signal, there may be ideas in the eyes of the knotted row of Fur'є:
,
De C i - important coefficients,
J i – orthogonal folding functions (basic functions).
For basic functions, you may need to think:
As a signal with intervals between t 1 and t 2, then
The norm of the basic function.
Since the function is not orthonormal, it can be brought in such a rank. With the increase in n, C n changes.
Assume that the impersonal basic functions (j n ) are inserted. When given impersonal basic functions and when fixed quantity warehouses in the narrowed Fur'є row, the Fur'є row gives an approximation of the external function, which may have a minimum mean-square pardon for the designated external function. Uzagalneniy row Fur'є yes
Such a row gives a minimum to the average pardon (kidney).
Є 2 task of placing the signal on the simplest functions:
^ More precisely, layout on the simplest orthogonal functions (Analytical model for the signal, analysis of the behavior of the signal).
^ Approximation of process signals and characteristics if it is necessary to add to the minimum the number of members of the specified row. They lie before them: the polynomials of Chebishev, Ermit, Legendre.
^ Harmonic analysis of periodic signals
When expanding a periodic signal s(t) into a Four's series for trigonometric functions, as an orthogonal system, take
The interval of orthogonality is determined by the norm of the function
The mean value of the function in the period.
- basic formula for
vyznachennya a number of Fur'є
The module is a paired function, the phase is an unpaired function.
Let's look at a couple for up to the dick
- layout next to Four'e
^
Apply spectra of periodic signals
Straight cut. Podіbne kolyvannya, often called meander(Meander is a Greek word that means “ornament”), to know a particularly wide range of vimiryuvalnoe technique.
Let the signal s(t) of the tasks look like an active function, as it looks like zero in the interval (t 1, t 2). This signal can be integrated.
Let's take some time interval T, which includes an interval (t 1, t 2). Todi. The spectrum of a non-periodic signal is strong. The task signal can be given at the sight of the Four'e row 
, de
On the basis of which we take:
Oskіlki T®µ then the sum can be replaced by the integration, and W 1 by dW and nW 1 by W. In this way, we pass to the Fur'e
,
de - spectral width of the signal. If the interval (t 1 t 2) is not specified, the integral may not be limited between. Tse zvorotne and direct transformation of Fur'є, obviously.
How to compare the difference for the outgoing sucile spectrum (the modulus of the spectral width) of the non-periodic signal and the outgoing line spectrum of the periodic signal, you will see that the stench is zbіgayutsya shape, but ripples scale 
.
Also, the spectral width of S(W) can't have all the main powers of the complex Four's series. That is, you can write down, de
, a 
.
Spectral thickness module 
є unpaired function and її can be considered as an amplitude-frequency characteristic. Argument 
- unpaired function, which is viewed as a phase-frequency characteristic.
On the basis of which signal, you can see it like this
From the pairing of the module and the unpairedness of the phase, the pidintegral function in the first section is paired, and in the other - unpaired W. The other integral is also equal to zero (unpaired function in the paired boundaries) i .
It is significant that at W=0 the spectral width is more flat under the curve s(t)
.
^
Powerful transformation of Fur'є
Sound signal at the hour
Let the signal s 1 (t) have a sufficient form of the spectral width S 1 (W). When the signal is blocked for the hour t0, a new function for the hour s2(t)=s1(t-t0) is taken away. Spectral Width signal s 2 (t) will be approached 
. Let's introduce a new change. Zvіdsi 
.
Whether a signal has its own spectral thickness. Suv the signal of the clock to bring up the change of the first phase, and the modulus of the first signal does not lie in the position of the signal on the clock.
^ Changing the scale of the hour
Let the signal s 1 (t) follow the clock. A new signal s 2 (t) of ties from the last spivings.
Trivality of the impulse s 2 (t) in n times is less, lower than the output. Spectral width of the squeezed pulse 
. Let's introduce a new change. We take it.
When the signal is squeezed n times, the band expands once in a while. The modulus of the spectral thickening changes in n times. When the signal is stretched in the hour, the frequency of the sounding of the spectrum and the increase in the modulus of the spectral thickness may be affected.
^ Change to the range of colivans
We multiply the signal s(t) by the harmonic signal cos(w 0 t+q 0). The spectrum of such a signal
Rozіb'ёmo yogo for 2 integrals.
Otrimane spіvvіdnoshnja can be written in the offensive form
In this way, the multiplication of the function s(t) on the harmonica can lead to a splitting of the spectrum into 2 parts, shifted by ±w 0 .
^ Differentiation and integration of the signal
Let the signal s 1 (t) be given from the spectral width S 1 (W). Differentiation of which signal 
give respite 
. Integration 
bring to viraz 
.
^ Folding signals
When the signals s 1 (t) and s 2 (t) are folded, the spectrum S 1 (W) and S 2 (W) is controlled by the spectra S 1 (W) and S 2 (W) to the total signal s 1 (t) + s 2 (t) S 2 (W) (because Four's transformation is a linear operation).
^ Dobutok two signals
Come on. This signal needs a spectrum
Let us represent the functions of the Fourth integrals.
Substituting another virase integral for S(W) is taken
Otzhe 
.
That is, the spectrum of dobutut two functions to an hour more expensive than their spectra (with a coefficient of 1/2p).
Yakscho 
, then the spectrum of the signal will be 
.
^ Mutual turnover of frequency that hour
at the converted Fur'є
Come on s(t) is a pair function just in time.
Let's assume that s(t) is a pair function. Let's write s(t) at the sight
. I will replace W by t and t by W, take it 
. Just as the spectrum has the shape of such a signal, then the signal in the same spectrum repeats the shape of the spectrum of a similar signal.
^
Expanded the energy of the spectrum of a non-periodic signal
Let's look at the viraz, for example f (t) \u003d g (t) \u003d s (t). And here this integral is more advanced. Tse spіvvіdnoshennia is called the jealousy of Parseval.
Energetic rozrahunok smugi pass: 
, de 
, a 
.
^
Apply spectra of non-periodic signals
Rectangular impulse
Signed by viraz
We know the spectral width
.
When lowering (expanding) the impulse between zeros shortens, the value of S (0) increases with it. The modulus of the function can be as the frequency response, and the argument as the PFC of the spectrum of a rectilinear pulse. Skin change to the sign of the upper phase of the phase on p.
When the hour is not visible in the middle of the pulse, as in the front of the PFC of the spectrum, the pulse can be supplemented with an additional edge, the damage to the pulse is temporary (the resulting PFC is shown by a dotted line).
Call-like (gaussian) impulse
Viznayetsya viraz. Constant and maє sens half of the trivality of the impulse, as it is determined on the level of e-1/2 in the form of the amplitude of the impulse. In such a rank, there is complete trivality for the impulse.
Spectral width of the signal 
.
For clarity, additionally show the step up to the sumi square 
, de value d 
stars. In this way, virase for spectral width can be brought to the point of view 
.
Passing to the new change 
taken 
. Vrahovyuchi, what is the integral, what to enter at the whole virus, dorivnyu, residually taken 
, de 
.
Impulse spectrum width
Gaussian momentum and th spectrum are manifested by the same functions and may have the power of symmetry. For the new speed of the volatility of the impulse and the smog of the transmission, it is optimal, so with a given torpidity of the impulse, the Gaussian impulse may have the minimum smog of the transmission.
delta pulse (single pulse)
Signal of tasks to sleep 
. Її it is possible to take away from resurrecting more impulses with a path of aspiration t і to zero.
Apparently, the spectrum of such a signal will be constant (the whole area of the impulse, which will be more alone).
To create such an impulse, all harmonics are needed.
Exponential impulse
Signal of the form c>0.
The spectrum of the signal is known as
Let's write the signal in another form 
.
Yakscho something. Tse means that we have a single haircut. At 
Virase is required for signal spectrum 
.
Star module
radio signals
Modulation
Let the signal be given, in the new A (t) - amplitude modulation, w (t) - frequency modulation, j (t) - phase modulation. Two stops satisfy the cutoff modulation. The frequency w is due to the great highest frequency spectrum to the signal W (the width of the spectrum, which deals with the details).
The modulation of the modulation may be the spectrum, the structure of which is to be found as a type of the spectrum of assistance that is transmitted, so in the form of modulation.
You can use the number of types of modulation: interruptless, pulse, code-pulse.
^
Amplitude modulation
Zagalny viraz for amplitude-modulated colivannya looks like this
The nature of the envelope A(t) is determined by the type of message that is being transmitted.
As a wake-up signal, you can see the light of a modulated call. De W is the modulation frequency, g is the outgoing phase, k is the proportionality coefficient, DA m is the absolute change in the amplitude. Setting 
- Modulation coefficient. Vikhodyachi z tsogo can be recorded. Todi amplitude-modulation kolyvannya recorded with such a look.
In case of non-conjugated modulation (M? 1), the amplitude of the coercion changes in the range of 
before 
.
The maximum value is shown by peak tension. The average for the period of modulation is tightness.
The intensity of transmission of an amplitude-modulated signal is greater than that of transmission of a simple signal.
Spectrum of amplitude-modulated signal
Let the modulation be determined by viraz
Let's remake this viraz
First dodanok - no modulation colivanya. The other and the third are colivannya, which are in the process of modulation. Spectrum width 2W.
How is the signal є sum 
de , a . Why de 
.
Zvіdsi otrimaєmo
The skin from the warehouse spectrum of the modulating signal independently one and one suits two binary frequencies (left and right). Spectrum width in this direction 2W 2 = 2W max 2 maximum frequency of the signal that modulates.
On the vector diagram, every hour wraps around the annual arrow with the top frequency w 0 (the view is conducted on the horizontal axis). The amplitudes and phases of the pellusts must be equal to each other, so the resulting vector DF will be the directing vector along the line OD. The subcarrier OF vector changes only in amplitude, without changing its apex position.
Give me the signal Let's write it down in a different way.
The signal is given a spectrum 
, de , and SA is the spectral width of the light. Zvіdsi viplivaє residual viraz for the spectrum
This is explained by the strobe function of the d-function, so that all warehouses reach zero kr_m frequencies w±w n (these values for any d-function reach zero). For now, the spectrum is not discrete, everything is one and the same warehouse.
^
frequency modulation
Come on є kolyvannya іz frequency modulation. However, the frequency is the same as the phase. If you change the phase, the streaming frequency will also change.
frequency modulation
,
De є amplitude of frequency variation. For the sake of style, we call it frequency deviation or just deviation.
De w 0 t – current phase change; - Index of apex modulation.
Let's say de 
.
,
De m - modulation coefficient.
Thus, harmonic phase modulation with index is equivalent to frequency modulation with deviation.
With a harmonic modulating signal, a difference between CHS and FM can be detected, only changing the modulation frequency.
In case of emergency deviation W.
With FM, the value proportional to the amplitude of the modulating voltage and not to fall into the modulation frequencyW.
For a monochromatic modulating signal, phase-frequency modulation is indistinguishable.
^
The spectrum of the signal at the edge modulation
Come on
Є two amplitude modulation signals. So warehousing, like winding up quadrature warehouses.
Come on. Tse zbіgaєtsya s. Here q 0 = 0, g = 0.
Cos and sin - periodic functions and are arranged in a series of Fur'є
J(m) - Bessel function of the 1st kind.
The spectrum with cut-off modulation is infinitely large, on the vіdmіnu view of the spectrum with amplitude modulation.
When modulating at the top, the spectrum of frequency-modulated colivanation is formed when modulating with a frequency of 1, it consists of an undifferentiated number of harmonics, which are grouped by a carrier frequency.
Noodles: The spectrum is wide.
Advantages: the most exciting.
Let's look at the vipadok, if m<< 1.
If m is more than small, then in the spectrum there are only 2 bands of frequency present.
Spectrum width (m<< 1) будет равна 2W.
If m=0.5?1, then there is another pair of binary frequencies w±2W. The spectrum width is up to 4W.
If m=1¸2, there are third and fourth harmonics w±3W, w±4W.
Spectrum width at m more great
SHS = 2mW = 2w d
If the modulation coefficient is significantly less than one, then such modulation is called shvidkoy todi w d<< W.
If m>>1, then povіlna modulation, then w d >> W.
^
Spectrum of a radio pulse with frequency modulation
zapovennyam
, de
De, 
The main parameter of the line-often modulated signal (chirp) or the base of the chirp signal.
B can be positive and negative.
Assume that b>0
The signal spectrum has 2 components:
1 - burst close to the frequency w;
2 - surge close to frequency -w o.
With the assigned spectral width in the region of positive frequencies, another addition can be added.
Extending the exponent to a perfect square
, de С(х) and S(х) - Fresnel integrals
Module of spectral width of chirp signal
Phase of the spectral thickening of the chirp signal
The larger m, the closer the shape of the spectrum is rectilinear with the width of the spectrum . Phase deposition is quadratic.
With m right to large values, the shape of the frequency response is right-angled, and the phase is composed of two parts:
one). give a parabola
2). bend up to
With great m i: 
The same module values: .
Changed amplitude-frequency modulation
Spectral width of the cosine quadrature cosine 
at =0 will be
When assigned to the spectrum of sinus quadrature colitis 
phase cut should be adjusted to -90°. Otzhe,
In this way, the residual spectral strength of the coli is determined by virase
Passing to the change, otrimuєmo
.
The structure of the spectrum of the signal when the amplitude-frequency modulation is changed depends on the type of functions A(t) and q(t).
With frequency modulation, the phases of unpaired harmonics change by 180 °. One-hour modulation і for frequency, і for amplitude at the same time A(t) і q(t) lead to the destruction of the symmetry of the spectrum only in phase, but also in amplitude.
If q(t) is an unpaired function of t, then for any A(t) the spectrum of the output signal is asymmetric.
Let A(t) be a paired function, then A z (t) is a pair, A s (t) is unpaired, є purely speech, symmetric to W, paired, and - purely manifest, asymmetric to W and unpaired.
With the improvement of the multiplier j, the spectrum of the external coli is speech. The same result can be taken for an unpaired function A(t). In this way the spectrum is purely visible and unpaired.
For the symmetry of the output spectrum, it is necessary to have pairing q(t) for understanding that A(t) was either paired or unpaired like t. If A(t) is the sum of paired and unpaired functions, then the output spectrum is asymmetrical for any mind.
The phase of the chirp pair is the amplitude of the pair. 
And why 
The visual spectrum of views is symmetrical.
А(t) = pair function + unpair function, and q(t) - pair function.
.The spectrum of views is non-symmetric.
Vuzkosmogovy signal
Under it, it becomes clear whether there is a signal, which may be a lot of frequencies, is occupied by a signal significantly less than the carrier frequency: .
De A s(t) is the in-phase amplitude, U s(t) is the quadrature amplitude.
Complex amplitude of the ultrasonic signal 
.
,
De is a wrapper operator.
The simplest colivanya 
can be shown in the form 
de . In this case, oginayucha A (t) on the vіdmіnu A є function of the hour, as it is possible to calculate from the mind the saving of the given function a (t)
From which point it is clear that new functionА(t) is essentially not a “bending” for a sensibly accepted sense, so that it can bend the curve a(t) (replacement of the torso at the points, de А(t) may be the maximum value). That is why we incorrectly assigned the luminous frequency. The main method of mittev's frequency is Hilbert's method for the assignment of frequency.
Like a signal, then
What is the phase of the signal, and the mitteva frequency 
Physical lighting 
.
It is acceptable that the reference frequency was chosen not wо, but wо + Dw, then
de .
Perche
The module of the complex oginayuchoy is more expensive physical oginayuchoy and constant, do not lie in the choice of frequency.
friend the power of the complex oginayucho:
The module of the signal s(t) must be less or more us(t). Evenness is present only if cos w o t = 1. At qi, the moment is similar to the signal and the light is similar.
The physical threshold is adjusted to the maximum signal amplitude.
Knowing the complex signal, you can know the її spectrum, and through it the signal itself.
,
.
Knowing G(w) we know Us(t).
Multiply by (-b-jt) 
, 
. Sound amplitude will be 
.
^
Analytical signal
Send the signal s(t), which will be shown as 
. Let's distribute yoga in two warehouses 
.
That one has a virazi 
- analytical signal. If you want to enter a change, then . Tobto we took away 
. Real signal є 
, a signal of engagement for Hilbert 
. Analytical signal є 
.
, 
- Direct and reverse transformation of Hilbert.
Designation of bearing and bending behind the Hilbert method
Signal amplitude 
, yoga phase 
. The value of the miter frequency 
.
Butt: . .
- More precisely, the appointment of an oginayucho. Using the Hilbert method allows you to give unambiguous and absolutely reliable values of the outgoing frequency to the signal.
- If any signal can be spread in a row Fur'є.
- Hilbert success signal.
If the representation signal is the Four's order, and the Four's integral, then the same 
, 
.
^
The power of the analytical signal
The addition of the analytical signal z s (t) to the binding of the other signal z s * (t) is equal to the square of the outgoing (physical) signal s (t).
Otherwise de.
Hilbert's transformation for the Vuzkosmog process
Give me some good luck according to Hilbert signal 
.
Vihodyachi z ogo otrimaєmo
Powerful transformation of Hilbert
– Hilbert's transformation, de H() – transformation operator. 
butt. The signal s(t) is an ideal low-frequency signal.
Frequency and clock characteristics
radio engineering lancers
Let me have a linear active chotiriplus.
1. Transfer function 
. Characterizes the change of the signal at the output similar to the signal at the input. The module is called amplitude- frequency response chi is just a frequency response. The argument is the phase-frequency characteristic, or simply the phase.
2. Impulse response 
- Reaction of a lansyug to a single impulse. Characterize the change in the signal at the hour. The connection with the transfer function is made through the turnaround and the direct transformation of Fur'є (vіdpovіdno) 
. Abo through the transformation of Laplace 
.
3. Transitional function - the reaction of the lancet to a single strobok. Cost of accumulated signal per hour t.
^
Aperiodic pidsiluvach
Scheme of substitution of the simplest aperiodic pidsiluvach. Subsidiary appropriation of representations in the view of the dzherel strum SE 1 from the internal conductivity G i =1/R i . Mistk_st C includes the interelectrode capacitance of the active element and the capacitance of the outer lance, which shunts the navantage resistor R n.
The transfer function of such a switch
,
de S is the coolness of the active element, E 1 is the input voltage.
Maximum strength coefficient (at ) 
. Zvіdsi 
de - the hour of the hustle.
Transmission module 
- AFC. That is, the signal is passed through less at singing smooth frequencies. PFC - 
.
Vision third, reworked and supplemented
Approved by the Ministry of Higher and Secondary Special Education of the SRSR as a tutor for students of radio engineering specialties of universities
MOSCOW "Radyanske radio" 1977
The book was handed over to the course "Radiotechnical lances and signals" for universities of radiotechnical specialty. At the link with the requirements of the new program, the data has been thoroughly modified and supplemented with such new divisions: discrete digital processing of signals; approximation of processes and characteristics by Walsh functions; synthesis of radio engineering languages
Particular respect was given to divisions dedicated to statistical phenomena of radio engineering lancers. Methodically reworked from the spectral and correlational analysis of deterministic and vertical signals, as well as from the theory of their transformation in linear, parametric and non-linear extensions.
If the book is recognized for students of radio engineering faculties of universities, it may also be relevant to a wide range of fahivtsiv, as it is practiced at the radioelectronics school and at the modern schools of science and technology.
Gonorovskiy I. S. Radiotechnical lancers and signals. A handyman for cherries. View. 3-th, revised. that dod. M., "Glad. radio”, 1977, 608 p.
Moving to the third meeting
Chapter 1. INTRODUCTION
1.1. The main halls of the radio engineering
1.2. Transmission of signals to the station. Peculiarities of widening radio waves and frequencies, which are victorious in radio engineering
1.3. Basic radio engineering processes
1.4. Analogue, discrete and digital signals and signals
1.5. Radiolancers and methods of analysis
1.6. The problem of susceptibility to the communication channel
1.7. Head of the exchange rate
Chapter 2. SIGNALS
2.1. Zagalni respect
2.2. Distribution of a sufficient signal for a given system of functions
2.3. Harmonious analysis of periodic splittings
2.4. Spectra of the simplest periodic colivings
2.5. Pain relief in the spectrum of periodic colitis
2.6. Harmonious analysis of non-periodic splittings
2.7. Acts of power and reincarnation of Fur'є
2.8. Increased energy in the spectrum of non-periodic colitis
2.9. Apply the designation of the spectra of non-periodic coliving
2.10. Spivvіdnoshnja between trivalіstyu signal and the width of the th spectrum
2.11. Infinitely short impulse from a single area (delta function)
2.12. Spectra of possible nonintegrated functions
2.13. Submission of signals on the area of complex change
2.14. Giving signals with a swirling frequency swirl at the sight of Kotelnikov's row
2.15. Theorem of consequences for the frequency domain
2.16. Correlation analysis deterministic signals
2.17. Spivvіdnennia between the correlation function and the spectral characteristic of the signal
2.18. coherence
Chapter 3. RADIO SIGNALS
3.1. Zagalni vyznachennya
3.2. Radio signals with amplitude modulation
3.3. Frequency spectrum of amplitude-modulated signal
3.4. Cutoff modulation. Phase and mitteva frequency of colitis
3.5. The spectrum of colivannya under the hour of the apex modulation. Zagalni spіvvіdnoshennia
3.6. The spectrum of coercion with harmonic modulation
3.7. Spectrum of a radio pulse from frequency modulation
3.8. Spectrum of colivannya when changing the amplitude-frequency modulation
3.9. Originally, the phase and frequency of the ultrasonic wave signal
3.10. Analytical signal
3.11. Correlation function of modulating coagulation
3.12. Discretization of the VUV signal
Chapter 4. BASIC CHARACTERISTICS OF FALL SIGNALS
4.1. Global designation of vypadkovyh processes
4.2. See the vipadian processes. Apply
4.3. Spectral thickness of the tightness of the depression process
4.4. Spivation between the energy spectrum and the correlation function of the rebound process
4.5. Cross-correlation function and mutual energy spectrum of two rebound processes
4.6. Vuzkosmugovy vpadkovy process
4.7. Colivannya, modulated by the amplitude of the vibrational process
4.8. Colivannya, modulated by the phase of the vipadkovy process. Strength of imovirnost
Chapter 5
5.1. Introductory respect
5.2. Appointment and main power of the active lancer
5.3. Active chotiripole as a linear subsilyuvach
5.4. Transistor switch
5.5. Pidsiluvach on an electronic lamp
5.6. Aperiodic pidsiluvach
5.7. Resonant pidsiluvach
5.8. Zvorotniy zv'azok in the active chotiripole
5.9. Zastosuvannya negative zvorotny link to improve the characteristics of the podsilyuvach
5.10. Stability of linear active lances with a ringing sound. Algebraic criterion of durability
5.11. Frequency criteria of resistance
Chapter 6
6.1. Introductory respect
6.2. Spectral method
6.3. Overlay integral method
6.4. Passage of discrete signals through an aperiodic substation
6.5. Differentiation and integration of signals
6.6. Peculiarities of the analysis of radio signals in the selected lancers. Approximation spectral method
6.7. Simplification of the overlay integral method (folding method)
6.8. Passage of a radio pulse through a resonant substation
6.9. Linear sedation with continuous amplitude modulation
6.10. Passage of phase-shift keying through a resonant lance
6.11. Passage of frequency-shifted colivannya through viborchiy lanceug
6.12. Passage of frequency-modulated coagulation through the selection of lances
Chapter 7
7.1. The transformation of the characteristics of the vipadic process
7.2. Characteristics of air noises in radio-electronic lancets
7.3. Differentiation of the vipadical function
7.4. Integration of the vipadical function
7.5. Normalization of depression processes in high-margin lancets
7.6. Rozpodіl sumi kolіvanіh kolivani іz vipadkovymi phases
Chapter 8
8.1. Non-linear elements
8.2. Approximation non-linear characteristics
8.3. Injection of harmonial colivans on lancets with non-inertia non-linear elements
8.4. Non-linear resonant power
8.5. Increased frequency
8.6. Amplitude exchange
8.7. Non-linear lancet from filtration fast strumu(straightening)
8.8. Amplitude detection
8.9. Frequency and phase detection
8.10. Signal frequency conversion
8.11. Synchronous detection
8.12. Otrimanya amplitude modulation coliving
Chapter 9. AUTOGENERATORS OF HARMONIOUS KOLIVAN
9.1. Autocolumn system
9.2. Viniknennya kolyvannya in autogenerator
9.3. Stationary oscillator mode Phase balance
9.4. M'yakiy that zhorstky modes of self-excitation
9.5. Apply autogenerator circuits
9.6. Non-linear alignment of the oscillator
9.7. Close proximity to the development of a non-linear leveling of the self-oscillator
9.8. Auto-oscillators with internal turn signal
9.9. Auto-oscillator with a line of zatrimka in the lances of the whirlpool
9.10. Diya harmoniynoi EPC on lanceuzi with a positive turning point. Regeneration
9.11. D_ya harmonic EPC on the oscillator. Frequency hoarding
9.12. Cutoff modulation in oscillator
9.13. YaS-generators
Chapter 10
10.1. General characteristics of lanceugs with changing parameters
10.2. Passage of colivane through linear lancets with changing parameters. transfer function
10.3. Modulation as a parametric process
10.4. Designation of the impulse response of the parametric lance
10.5. Energetic spіvvіdnoshennia in lanciug with non-linear reactive element at harmonic coliving
10.6. The principle of parametric reinforcement
10.7. Substitution circuit for capacitance and inductance, which change according to the harmonic law
10.8. Single-circuit parametric podsiluvach
10.9. Dual-frequency parametric podsiluvach
10.10. Frequency conversion behind the help of a non-linear reactive element
10.11. Vilni kolyvannya in contours with єmnistyu, scho periodically zminyuєtsya.
10.12. Parametric generators
Chapter 11
11.1. Zagalni respect
11.2. The transformation of the normal process in non-inertia non-linear lances
11.3. Reconstruction of the energy spectrum for a non-inertia non-linear element
11.4. Injection of high-cosmic noise into the amplitude detector
11.5. Spiral infusion of harmonic corollary and normal noise to the amplitude detector
11.6. Spiral infusion of harmonic corollary and normal noise to the frequency detector
11.7. The interplay of harmonic oscillation and normal noise in the amplitude intermediate with resonant interference
11.8. Correlation function and energy spectrum of the vypadkovy process in the parametric lanceug
11.9. Injection of the multiplicative shift to the law rozpodіlu signal
Chapter 12
12.1. Introductory respect
12.2. Uzgodzhena filtration given signal
12.3. Impulse response of a narrowed filter. Physical condition
12.4. Signal that overshoot at the exit of the narrowed filter
12.5. Apply a comforting filter
12.6. Shaping a signal tied to a given filter
12.7. Improved filtering of the given signal with low noise
12.8. Filtering the signal with an unknown cob phase
12.9. Improved filtering of the complex signal
Chapter 13. DISCRETE SIGNAL PROCESSING. DIGITAL FILTERS
13.1. Introductory respect
13.2. Discrete Sequence Algorithm (for clock area)
13.3. Discrete transformation of Fur'є
13.4. Signal discretization error
13.5. Discrete transformations of Laplace
13.6. Discrete filter transfer function
13.7. Recursive filter transfer function
13.8. Implementation of the r-transformation method for the analysis of discrete signals talants
13.9. z-reversal of thychas functions
13.10. z-transformation of transfer functions of discrete lances
13.11. Apply the analysis of discrete filters based on the z-reversal method
13.12. The transformation of analogue is digital. Noise quantization
13.13. A converted figure is an analogue of that renewal of a continuum signal
13.14. Svidkodiya arithmetic I will add a digital filter. Shumi rounding
Chapter 14
14.1. Entry
14.2. Orthogonal polynomials and functions of interruptionless type
14.3. Apply zastosuvannya non-permanent functions
14.4. Destination of Walsh functions
14.5. Apply a stopover of the Walsh functions
14.6 Mutual spectrum of basis functions of two different orthogonal systems
14.7. Discrete functions Volsha
Chapter 15
15.1. Introductory respect
15.2. Acts of power of the transfer function of the chotiriplus
15.3. Connection between the amplitude-frequency and phase-frequency characteristics of the chotiripole
15.4. Submission of a chotiri-pole of a cascading type to cascade connections of elementary choti-poles
15.5. Implementation of a typical layout in a different order
15.6. Implementation of the phase-correcting lancet
15.7. Features of the synthesis of a chotiripole for a given amplitude-frequency characteristic
15.8. Synthesis of the low-pass filter. Butterworg filter
15.9. Chebishev filter (low frequencies)
15.10. Synthesis of different filters based on the output low-pass filter
15.11. Sensitivity of the characteristics of the lancer to change the parameters of the elements
15.12. Imitation of inductance and auxiliary active DO-lance. Girator
15.13. Actual features of the synthesis of digital filters
Addendum 1. Signal from the minimum additional trivality for a range of frequencies
Addendum 2. Correlation function of the signal on the square hour - frequency
List of references
Smart designations
Subject indicator
PEREDMOVA TO THE THIRD VIDANNYA
The direct orientation of the assistant to the course "Radiotechnical lances and signals" is the basis of the first two languages, and is preserved by the others. However, the book has been thoroughly revised in order to ensure the need for new distributions, which modern development techniques of radio lanterns and signals.
A wide range of discrete and digital radio-electronic systems does not allow the exchange of the RTCiS course with the framework of only analog lances and signals.
The development of the technology of integrated microcircuits, the foundations on a wide variety of methods for the synthesis of lancets, does not allow the course of RTCIS to be combined with only methods for the analysis of lancets.
Nareshti, a strimke of penetration of statistical methods in all areas of radio engineering and electronics has a greater ground leveling of the power of vipadkovy signals and a transformation of their radio lanterns.
New divisions have been included in the svetlі tsikh vіdpovіdno before the new program of the RTCіS course until the manual: "Basic characteristics of vypadkovy signals" (ch. 4), "Passage of vypadkovy kolivans through linear lances with constant parameters" (ch. 7), "Discrete processing of signals . Digital Filters" (ch. 13), "Supporting the Collision with Special Functions", including the Walsh functions (ch. 14), "Elements of Synthesis of Linear Radio Lancets" (ch. 15). Newly written goal. 5, is dedicated to the theory of linear active lances with a back link.
Reshta of the heads of the forefront recognized the methodical reworks with the improvement of the introduction of the RTCIS course and the numerical recognition of the graduates of the radio engineering specialties of the universities, as well as the richness of the radio faculties.
It is primordial that in order to acquire the necessary knowledge of the first importance, the development of students from beginners to independent creative work is possible. It is clear to the decision of the XXV z'їzdu of the CPRS about the development of scientifically advanced work in the higher initial mortgages, the practice of educating students up to science robot. Therefore, the author has added the contribution of the main information, insurance on the cob and of the language of all students in radio engineering specialties, with the contribution of some supplementary, folding materials, insurance of students from advanced training. Such a distribution was seen by a petite. Insignificant shortness of time, which may be needed in the fall due to the equal theoretical and theoretical training of students, does not matter without damaging the consistency and integrity of the course.
The author writes to the students of the GRT Department of the Moscow Energy Institute prof. Fedorov N. N., associate professors Baskakov S. I., Bilousova I. V., assistant to Bogatkin V. I., associate professor Zhukov V. P., senior vikladachiev Ivanoviy N. N., associate professors Kartashev V. G., Mikolaev A M., Pollak B. P., senior vikladachev Shtikov V. V. for highly qualified that report reviewing the manuscript of this book. A great number of critical respects and valuable occasions helped to improve the quality of the work of the handicraftsman.
An invaluable help at the robot over the manuscript was given by vikladachi, specialists and graduate students of the Department of Radio Engineering of the Moscow Aviation Institute. In all of them, the author speaks deeply.
Download Gonorovskiy I. C. Radiotechnical lancers and signals. A handyman for cherries. The third edition has been redesigned and supplemented. Moscow, Vidavnitstvo "Radyansk Radio", 1977
Radiotechnical languages and elements that are victorious for zdijsnennya transfers in § 1.2, the conversion of signals and koliva, can be divided into the following main classes:
linear lancets with constant parameters;
linear lancets with changing parameters;
non-linear lances.
It should be pointed out that in real radio installations it is clear that linear and non-linear lances and elements are not always possible. The introduction of some and the same elements to linear or non-linear ones often fall into the same line of signals that are injected into them.
Prote induced more classification of lanciugs, the necessary lucid theory and signal processing techniques.
Formulate the main power of these kіl.
2. LINE LANTSYUGI WITH CONSTANT PARAMETERS
You can get out of such appointments.
1. Lance is linear, like elements that go in before the new, do not lie in the presence of strong forces (voltage, struma), which are on the lance.
2. Linear lancet follows the principle of superposition (overlay).
In mathematical form, this principle manifests itself in the following equivalence:
de L is an operator that characterizes the influx of the lancer on the input signal.
The essence of the principle of superposition can be formulated by the offensive rank: when dividing on a linear lance, a lot of oval forces, the behavior of a lance (strum, tension) can be marked as a way of overlay (superposition) solution, known for skin forces okremo. It is possible to beat the same formula: for a linear lance, the sum of effects in the case of a total of infusions is combined with the effect in the sum of the infusions. When you transfer, scho lansy is a vіlniy vіd pochatkovyh zapasіv energії.
The principle of superposition is the basis of the spectral and operator methods for the analysis of transitional processes in linear lances, and the method of superposition integral (Duhamel's integral). Zastosovuyuchi principle overhead, be-like folding signals of transmission їх through linear lines can be laid out in a simple way, convenient for analysis (for example, harmony).
3. Be-yakoy collapsible dії in a linear lance with constant parameters, do not blame the splitting of new frequencies. This is due to the fact that, with a harmonic influx on a linear lance with constant parameters, the sounding at the output is filled with a harmonic one with the same frequency, which is at the input; the amplitude changes less and the phase of colivannya. Having announced the signals on the harmonium ringing and presenting the results of the spreading (1.1), we reconsider that only a ringing with frequencies can be used at the output of the lancer, which can enter the warehouse of the input signal.
This means that it is necessary to change the signals, which are accompanied by the appearance of new frequencies (that is, the frequencies included in the spectrum of the input signal), cannot, in principle, be designed for an additional line stake with constant parameters. Such lancers know the widest zastosuvannya for the cherry of the day, not related to the transformation of the spectrum, such as linear signal strength, filtering (behind the frequency sign) and so on.
3. LINE LANTSYUGI WITH CHANGING PARAMETERS
The lancers are toiling in the air, one or more of the parameters of which change in the hour (but do not lie down at the input signal). Similar lancets are often called linear parametric.
Formulated at the front point of authority 1 and 2 are valid for linear parametric lances. However, on the view of the forward slope, the simplest harmonic infusion is created in the linear lance with the changing parameters of the folding, which makes the frequency spectrum. Tse can be explained on the stepping butt. Let's go to the resistors
donated EPC harmony
Strum via opir
Yak bachimo, at the warehouse of the stream there are components with frequencies, there are none. From the point of view of the simplest model, it is clear that by changing the hours of operation, it is possible to change the spectrum of the input signal.
An analogous result, although with more collapsible mathematical calculations, can be taken for the Lancer with changing parameters, in order to eliminate the reactive elements - inductance coils and capacitors. Tse food at the goal. 10. Here it is more significant that the linear lance with changing parameters transforms the frequency spectrum into the infusion and, then, there may be victories for certain transformations of signals, which are accompanied by the transformation of the spectrum. From afar, it will be seen that the periodic change in the hour of inductance or the capacity of the kolivalny lancet allows for some minds to “pump” the energy from the auxiliary building, which changes this parameter (“ parametric subsidiaries» and «parametric generators», goal. 10).
4. NON-LINEAR LANTSYUGI
Radiotechnical language is non-linear, so that only one or a few elements enter the warehouse, the parameters of which are equal to the input signal. The simplest non-linear element is a diode with a current-voltage characteristic, shown in fig. 1.4.
Let's list the main authorities of non-linear kіl.
1. Prior to non-linear lines (and elements), the principle of superposition does not stop. The power of the non-linear lines is closely related to the curvature of the current-voltage (or other similar) characteristics of the non-linear elements, which destroys the proportionality between the stream and the pressure. For example, for a diode, yakscho strum vіdpіdaє struma and nаpruzі - strum then the total voltage vіdpіdatime strum vіdminny vіd sumi (Fig. 1.4).
From this simple butt it is clear that when analyzing the injection folding signal on a non-linear language of yoga it is not possible to lay out more simply; it is necessary to send a signal to the resulting signal. Inconsistency for non-linear lances in the principle of superposition makes it difficult to spectral and other methods of analysis, based on the distribution of a folding signal in a warehouse.
2. The important power of the non-linear stake is the transformation of the signal spectrum. In case of a non-linear lance of the simplest harmonic signal in the lance, crimson of the fundamental frequency, the harmonics are blamed at frequencies that are multiples of the fundamental frequency (and in such vibrations, there is a constant warehouse stream or a voltage). Further on, it will be shown that when the signal is folded in a non-linear lance, the cream of harmonics, which is due to the combination of frequencies, which is the result of the interaction of the folds, which enters the warehouse signal.
At a glance, the transformation of the spectrum to the signal follows the principle of difference between linear parametric and non-linear lances. In a non-linear lance, the structure of the spectrum at the output lies only in the form of the input signal, and the second is the amplitude. In a linear parametric lance, the structure of the spectrum depends on the amplitude of the signal to fall.
Of particular interest for radio engineering is to establish free colivannya in non-linear lancets. Similar chimes are called self-oscillations, the shards of the stench blanch and can stably sound without a sour periodic infusion. Vitrata of energy is compensated by the energy of the constant strumu.
The main radio engineering processes: generation, modulation, detection and frequency conversion are accompanied by transformation frequency spectrum. Therefore, these processes can be developed for the help of either non-linear or linear parametric lances. In some vypadkas, non-linear lances are simultaneously victorious, so are linear parametric lances. In addition, it should be noted that the non-linear elements work together with the linear lances, which makes it possible to see the brown components of the converted spectrum. At zvyazku z tsim, as it was intended to be on the cob of this paragraph, rozpodіl lanzyugіv on linіynі, nіlіnііnі і і ііnіinіynі parametrical dosit wisely. Call for a description of the behavior of various nodes of one of that radio engineering outbuildings to be brought to the forefront of various mathematical methods - linear and non-linear.
Mal. 1.4. Current-voltage characteristic of a non-linear element (diode)
Vikladenі vische osnovnі vlastivostі lantsyugіv troh klasіv - lіnіynih of postіynimi parameters lіnіynih the parametrization i nelіnіynih - zberіgayutsya for whether yakih forms realіzatsії lantsyugіv: s zoseredzhenimi parameters of rozpodіlenimi parameters (lіnії, vipromіnyuyuchі pristroї) i r d Tsі vlastivostі poshiryuyutsya takozh i.. on the extension of digital signal processing.
Slid, prote, podkreshliti, scho of the provisions of the basis of the lances on the linear and non-linear principle of superposition of formulations is greater than the operation of summing up the signals at the entrance of the lancers [div. (1.1). However, this operation does not depend on modern signal processing systems. It is important for practice, for example, if the signal at the entrance of the lancer is an additional two signals. It appears that for such signals it is possible to create a processing that follows the principle of superposition, the processing will be specially selected non-linear and linear operations. Similar processing is called homomorphic.
The synthesis of such extensions is considered in the course (div. Ch. 16), after the development of linear and non-linear lines, as well as digital processing of signals, the development of such and became a post-production to a wide distribution of homomorphic processing.
