See signals, like radio communication systems. Radio engineering signals. Theory of signals. Classification. Main characteristics of signals Elements of the general theory of radio engineering signals
.
Fundamentals of digital signal processing (DSP).
Vikladach: Kuznetsov Vadim Vadimovich
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Power supply. Radio engineering signals. Classification.
Signals can be voltage, strum, field strength. Most often, the wearers of radio technical signals are electromagnet colivannya. The mathematical model of the signal should be called the functional fallow, the argument is that it is an hour (the fallow of the voltage in the lane at the hour). For determining signals on the basis of a mathematical model, you can find out about the mitigation of the signal value at any given moment. The butt of a deterministic signal is a sinusoidal voltage f=50Hz w=314s^-1.
Impulse signals are less likely to appear in the midst of the final hour. Apply impulse signals: video impulse (Fig. 2a) and radio impulse (Fig. 2b).
As the physical process generates a signal, it develops at the hour in such a way that it can be overcome at any time, the signals of this class are called analog. An analog signal can be shown by a graph of the same time as an oscillogram.
Discrete signals are described by a sequence of observations through equal intervals of an hour. The butt of a discrete signal is shown in small 3.
Digital signals are distinguished by a variety of discrete ones. Vіdlіkovі values appear as numbers. Ring out the victorious double numbers from the deaco rozmirnistyu. An example of a digital signal is given in Table 1.
Analog signals.
Periodic signal S(t), period T may come power: S(t)=S(t±nT) n=1,2,.
The period of the alarm signal with a frequency f and a circular frequency w to the upcoming sp_v_dnoshnennia: f=1/T=w/2π. Other applications of periodic signals are shown in small 5.
Power supply. Modulation signal. Fundamentals of modulation.
For a modulated signal, the amplitude, frequency and phase of a sinusoidal high-frequency signal change the cycle from low-frequency. The low-frequency signal is superimposed on the carrier.
1. Amplitude modulation (AM).
S(t) - audio signal - RF signal that you carry, M - modulation coefficient.
The butt of the modulated signal of the testimony of the baby 6.
2. Frequency modulation (FM: FM). The carrier amplitude remains constant, and the frequency of the carrier changes with the modulated signal.
An oscillogram of a frequency-modulated signal is shown in small 7.
3. Phase modulation (FM: PM). . The oscillogram of the FM signal shows little 8.
Under the positive hour of the period, the phase of the modulation of the pulse is shifted along the phase of the pulse of the carrier frequency, during which period the pulse changes and the frequency increases. Under the hour of the negative period of the modulating voltage, the phase of the modulating chirp changes in phase to the chirp of the carrier frequency. In this order, FM is one hour and emergency. For emergency situations, a reversal is fair: frequency modulation is single-hour phase modulation. FM zastosovuetsya at professional radio communication.
Sigma and delta functions.
The sigma function is defined by the upcoming virase:
Delta function is an impulse of infinitely large amplitude and infinitely small trivalence. (Fig. 10).
The delta function is similar to the sigma function.
If a signal is given by a continuous function multiplied by a delta function and integrated in hours, then the result will be a mitigation of the signal value in a point, de delta-impulse of the measurements.
From the powers of the delta function, which filter, the scheme of vimiruvach of the mitt value of the signal.
Sigma and delta functions are designed to analyze the passage of analog and digital signals through linear systems. The response of the system, which has a delta-impulse applied to it, is called the impulse response of the system H(t).
Power supply. The tension and the energy of the signal.
If not a constant voltage is applied to the resistor, but a changing signal s(t), then the tension will be changed by itself (mitteva tension).
Theoretically, the signal should sound that R=1. w=s(t)^2. To know the energy of the signal, it is necessary to integrate the intensity over the entire range;
For non-skinned signals in the hour, the average tension can be calculated as follows:
W=[W], E=[(V^2)*s]
The same energy is seen on the resistor with a support of 1 ohm, even though the voltage s (t) is applied before the new one.
If the signal is compared to the current T-interval, then the average intensity of the signal is considered.
Spectral analysis of signals.
Power supply. Razkladannya analog signal to a number of Fur'є.
An example of filing a saw-like signal in the presence of a sum of sinusoidal signals with a different amplitude and phase of representations in fig. 12.
We introduce the main frequency of the periodic signal with the period T: w_1=2pi/T. A periodic signal when deployed in a series of Four's is represented by a sum of sinusoidal signals or harmonics, with multiple frequencies of the fundamental frequency: 2w_1, 3w_1 ... The amplitudes of these signals are called the distribution coefficients. A number of Four's are written in the form of sumi harmonics:
Speech form low Four'є:
Vikoristovuyuchi in the form of writing in the course of electrical engineering as a complex number, the Fur series is represented as:
All virases have harmonics with negative frequencies. Negative frequency - tse physical understanding, won po'yazana zі way of representing complex numbers. If the sum of the harmonics can be a real number, then the skin harmonics will be complexly related to the harmonic –ω. For the absolute value of the amplitude of the harmonics with positive and negative frequencies equal.
Power supply. Spectral diagrams.
Distinguish amplitude and phase spectral diagrams. Harmonic frequencies are shown along the horizontal axis, and amplitudes (phases) along the vertical axis. If the modulus of the Four's series is shown in the complex form, then along the X axis do they show positive and negative circular frequencies?
An example of the spectrum of an analog periodic signal. (PWM)
Let's look at the sequence of rectilinear pulses from the period T, trivality τ and amplitude A.
Dobre.
The oscillogram of such a signal is given a little 13.
Postiyna warehousing of a direct signal.
bn = 0.
The spectral diagram for the sequence of rectilinear pulses is shown in fig. fourteen.
From the spectrum, the diagrams show that with an increase in spalling, the pulse trivality changes. The sequence of straight-cut pulses has a richer spectral warehouse, the spectrum has more harmonics and more amplitudes. In this order, the shortness of the trivality of the impulse to lead to the expansion of the spectrum. Signals from a wide spectrum can create crossovers.
The charges are low. Four'є to go through for additional mathematical packages.
The transformation of Fur'є.
The expansion of the area of acceptable signals is stopped.
Rozrіznyayut straight that zvorotne transformation.
Power supply. Direct conversion (transition from the signal to the spectrum).
Let s(t) - a single impulse signal of the end of the trivality. It is supplemented with the same, periodically advancing signal, with a period of T. We take away the sequence of impulses (Fig. 15).
In order to go to the transformation of Fur'є and to know the spectrum of a single impulse, it is necessary to know the boundary view of the Four'є series in complex form at
Razrahunok spectrum:
The physical dimension of the spectral width is affected by the fact that it is a coefficient of proportionality between a long small frequency interval Δf near the frequency f 0 and the amplitude of the harmonic signal with the frequency f 0 . The signal s(t) is composed of impersonal different sinusoidal signals in a small amplitude. The thick spectrum shows the contribution of the elementary sinusoidal signals to the skin frequency.
The spectrum of thickening of humility is represented by a complex number and is represented by a curve on the complex plane.
Diysna kіlkіst - amplitude spectrum
The spectrum of tightness
Phase spectrum
Powerful transformation of Fur'є
Linearity - the spectrum of the sum of the number of signals multiplied by the constant coefficient of the sum of the signals. If the signal amplitude changes by a factor, then the spectral width also changes by a factor.
The dominance of speech and visible parts of the spectrum. Speech is part of the spectrum, so the amplitude spectrum is a pair function of frequency. Amplitude spectrum is symmetrical around zero frequency. The visible part of the spectrum is an unpaired function of frequency. The phase spectrum is antisymmetric to zero frequency.
Misplaced signal at the hour. When sounding a signal at the hour, the amplitude spectrum does not change, and the phase spectrum shifts in phase.
Spectrum of dobutku signalіv dorіvnyuє zgortsі spektrіv i navpaki.
Power zastosovuetsya to the signal at the exit, as if the frequency response is visible.
The line system and signals on її inputs and outputs are shown on the little 20.
Delta function range.
In the delta-impulse range, all frequencies from 0 to .
Spectrum of the similar integral.
Zv'yazok іz ranks Fur'є.
Knowing the transformation of one period of a periodic signal, it is possible to calculate its expansion to the Fourier low.
An example of calculating the spectrum of an impulse signal.
Let's calculate the spectrum of a rectilinear video pulse with amplitude and trivality. The impulse of stowing is symmetrical to that of the ear (Fig. 22).
Passing in the form of a circular frequency up to the frequency f.
Amplitude spectrum of readings (Fig. 23).
Phase spectrum of readings (Fig. 24).
The spectrum of tension of indications (Fig. 25).
Power supply. Zvorotne transformation Fur'є.
Umov's basis of the spectral thickening of the signal.
Spectral analysis of the integration of signals.
The signal can be equalized by the spectral width, so that the signal is absolutely integrated.
Before an absolutely integrated signal, there is no harmonic ringing and steady stream.
Apply absolutely integrated and non-integrated signals to (Fig. 16).
The spectra of such signals are obtained through delta functions.
The spectrum of the signal of constant level A is the delta-impulse, the expansion at zero frequency ().
Physical Sensing Virase - a signal that is constant behind the module and over the hour may be constant warehouse only from zero frequency.
The spectrum of a sinusoidal signal.
If it is a periodic signal, you can detect Four's order in a complex form, so that you can see a sum of sinusoidal signals.
The spectra of the steady stream, sinusoidal and periodic signal are shown in (Fig. 17).
On a spectrum analyzer, the spectrum of a periodic signal can be seen in the sequence of guest pulses. The amplitudes of these impulses are proportional to the amplitudes of the harmonics. Typical view of the spectrum of representations (Fig. 18).
Spectral analysis can be carried out to the point of falling signals. You can see the spectrum of tightness. For example, a white noise can be seen (Fig. 1).
The first step is to proceed to the development of new phenomena, processes or objects, in science to begin to practice 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 for 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. A report about the series was made to understand further. sound described by one (single-dimensional signal; n = 1), two
(two-world signal; n = 2) or more (multiple signal n > 2) independent changes. Single-mode signals with functions for more than an hour, but richer-scale ones, more, dictate positions in the n-world expanse.
Fig.1. Classification of radio engineering signals
For the sake of simplicity, it will be necessary to consider, for the most part, one-time signals that lie in the hour, the material of the initial helper is allowed to be aggravated and to a rich, if the signal is given at a sighting point, or an inexhaustible mass, for example, in the camp of an hour. In television systems, the signal of a black-and-white image can be seen as a function f (x, y, f) of two space coordinates i hour, which sets the intensity of vibration at point (x, y) at the time hour 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 voltages on the fasteners of a rich pole (Fig. 2). Rich signals are described by collapsible functions, and their processing is most possible in digital form. Therefore, the rich models of signals are especially different in different situations, if the functioning of folding systems is analyzed using additional computers. Also, rich, or vector, signals are added up from anonymous one-dimensional signals
de n – whole number, signal size.
R 
ic. 2. The system of springs of the bagatopole
Due to the peculiarities of the structure of the time representation (Fig. 3), all radio technical signals are subdivided into analog (analog), discrete (discrete-time; in Latin discretus - divisions, divisions) and digital (digital).
If a physical process that generates a one-way signal can be detected by a continuous function for an hour u(t) (Fig. 3, a), then such a signal is called analog (uninterrupted), otherwise, it is narrowed, continual , 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 temporal 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. The butt of the analog signal is a voltage deac, as it is applied to the input of the oscilloscope, after which on the screen there is a continuous 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. It would be more correct to call interruption-free signal processing those that today 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 a temperature sensor, which can see the value of the skin 10 min, serve as a signal dungeon, uninterrupted for the values, but discrete for the 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 that is reversed before 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 іnformatsiї (zocrema, discrete signals of 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-interruptible alerts - non-interruptible 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 a set of discrete signals can be used to send a continuous signal to a single input of basic information, but we don’t know anything about the behavior of the signal in the intervals between the signals. However, using the class of analog signals, for such use of information it is practically not possible, and therefore the stench can be with a high degree of accuracy of observation of the values of 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 
quantize the scale by equal (small 3, c) and then replace the quantization of the discrete signal with numbers 
most often implemented in a double code, which is high (one) and low (zero) equal voltage potentials - short pulses trivality 
(Fig. 3, d). Such a code is called unipolar. Oscilki vidlіki can nabuvatye 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 it seems to be rounded. Pardons of rounding, which are blamed for what, 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 up the sequence, i.e., the values of the signal around (discrete) moments and hours, are called digital signals to the signal (samples). The given quantized value of the signal is presented as a set of pulses, which characterize zeros (“0”) and ones (“1”) when a value is given in a two-digit 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 of digital processing, nothing "physical" will come out, only a number. 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) if necessary, it can be converted back, to a voltage or a 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, when analyzing and processing signals, in most cases digital signals are replaced by discrete ones, and their intelligence in digital ones 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 boldly said that discrete signals are processed in discrete and digital channels (zocrema, in digital filters), rather than the middle structure of digital channels and signals are represented by numbers.
The number of attachments used for signal processing can operate with digital signals. It is also based on extensions, prompted more importantly on the basis of analog circuitry, as if they are 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 the mathematical appearance (beyond the level of a priori manifestation, in lat. a priori - from the front, i.e., supplementary information), all radio engineering signals are divided into two main groups: deterministic (regular; determined) and sufficient (Fig. 4).
Determinants are called radio engineering signals, mittevni znachennya such at some point in time, it is reliable to see, so that they transfer from ymovirnistyu, that they are lonely. 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 applications 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 this, it should be mentioned as a vipadkovy podії (or vipadkovі functions, vipadkovі values). 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 engineering 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.
Rice. 4. Signal:
a - determinations; b - vipadkovy 
Deterministic signals are subdivided into periodic and non-periodic (impulses). The signal of the end energy, which is exactly the same as zero for a short period of time, which can be equal to the hour of the completion of the transitional process in the system, for the injection on the basis of the wine assignments, is called an impulse signal.
Signals are called vipadkovymi, mittiev meanings of 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 the thermal imager, which is directly connected to the IR-vibration cord, 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). Although it is paradoxical at first glance, but a signal that carries basic information, it may be less than a vicious 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 vipadical processes, that and їх are described by additional methods, similar to the methods of describing the vipadical processes.
In the process of transmitting core information, radio engineering signals can be supported by another transformation. Tse sound in their names: modulation, demodulation (detection), encoded (decoded), enhanced, truncated, sampled, quantized and other signals.
For recognition, as signals may be in the process of modulation, they can be divided into modular (the first signal, which modulates the non-switching) or modulation (non-switching).
For belonging to a different kind of radio engineering systems, systems of transmission of information, separation of “communications”, telephone, telegraph, radio, television, radiolocation, radionavigation, vimiruval, signaling, services for this .
A short classification of radio technical signals has been introduced, which does not overwhelm their diversity.
As a carrier, high-frequency electromagnet ringing (radio waves) in a similar range is increased, buildings are expanded in large numbers.
The oscillation of the carrier frequency, which is changed by the transmission, is characterized by: amplitude, frequency and cob phase. In the mind, it seems like:
i = I m sin(ω 0 t + Ψ 0),
de: i- Mitteve meaning struma of a non-bearing kolyvannya;
I m- Amplitude of the struma of the bearing chiselling;
ω 0 - Kutova frequency nesuchy kolyvannya;
Ψ 0 – cob phase of bearing colivannya.
Primary signals (transmitted messages, converted into electrical form), which control the transmission robot, can change one of these parameters.
The process of managing the parameters of a high-frequency stream following an additional primary signal is called modulation (amplitude, frequency, phase). For telegraph types of transmissions, the term manipulation is used.
At radio communication, for the transmission of information, radio signals are installed:
radiotelegraph;
radiotelephony;
phototelegraph;
telecode;
folding view signals
The radiotelegraph connection is subject to: for the method of telegraphing; for the method of manipulation; stosuvannya telegraph codes; for the method of vikoristannya radio channel.
Depending on the method and speed of transmission, radiotelegraph communications are sent manually and automatically. In case of manual transmission, the manipulation is performed by a telegraph key from the MORSE code. The speed of the transmission (with auditory reception) becomes 60-100 signs per whilin.
In case of automatic transmission, the manipulation is carried out by electromechanical attachments, and by the reception of other devices for assistance. The speed of transmission is 900-1200 signs per note.
Following the method of choosing a radio channel, telegraph transmissions are transmitted on single-channel and rich-channel channels.
Behind the method of manipulation to the widest telegraph signals, there are signals with amplitude shifting (AT - amplitude telegraph - A1), with frequency shifting (ChT and DCT - frequency telegraphy and floating frequency telegraphy - F1 and F6), with phase shifting - F1 and F9) .
For jamming of telegraph codes, telegraph systems with the MORSE code are victorious; start-stop systems with 5 and 6 digit codes and others.
Telegraph signals are a sequence of straight-cut impulses (possessions) of the same or different trivality. The hireling for trivality is called elementary.
Main parameters of telegraph signals: telegraph security (V); manipulation frequency (F);width spectrum (2D f).
Shvidkist telegrafvannya V more number of elementary parcels, which are transmitted in a second, are transferred in bauds. With a telegraph rate of 1 baud for 1, one elementary parcel is transmitted.
Frequency of manipulation F numerically more than half of the speed of telegraphing V and win at hertz: F=V/2 .
Amplitude-manipulation telegraph signal ma spectrum (Fig. 2.2.1.1), in the same kr_m carrier frequency, to avoid the absence of frequency storage, spreading on the sides in front of it, with intervals equal to the frequency of manipulation F. warehouse range, roztashovanih on the sides of the vіd bearing. Thus, the width of the spectrum of the amplitude-shifted telegraph signal of the RF signal is 6F. The greater the frequency of manipulation, the wider the spectrum of the RF telegraph signal.
Rice. 2.2.1.1. Timchasovy and spectral feed to the AT signal
At frequency manipulation The strum in the antenna does not change in amplitude, but only the frequency changes, depending on the change of the manipulating signal. The spectrum of the signal FT (DFT) (Fig. 2.2.1.2) is like a bi spectrum of two (chotiriox) independent amplitude-shifting colivations with their own non-transmitting frequencies. The difference between the frequency of the onslaught and the frequency of the onslaught is called the separation of frequencies, is indicated ∆f and can be between 50 - 2000 Hz (mostly 400 - 900 Hz). Spectrum width for the FT signal is set to 2∆f+3F.
Fig.2.2.1.2. Time clock and spectral feed to the FET signal
To increase the throughput capacity of the radio line, rich channel radiotelegraph systems are installed. Stinks on one non-sense radio frequency, you can transmit two or more telegraph programs at the same time. The systems are separated from the frequency narrowing of the channels, from the time interval of the channels and the combination of the system.
The simplest two-channel system is the system of floating frequency telegraphy (DFT). Signals, frequency manipulation in the DCT system are transmitted by changing the carrier frequency by passing a one-hour burst on a new signal in two telegraph devices. At the same time, those who signal two devices, who work at the same time, can mother less than chotiri on the transfer of parcels. With this method, at some point in time, a signal of one frequency is vibrated, which confirms the singing of the manipulation of voltages. The priymalny annex has a decoder, with the help of which telegraph messages of constant voltage are formed by two channels. Strengthening the frequency of the fact that the frequencies of the other channels are distributed in different areas of the global frequency range and all channels are transmitted at the same time.
When timchasovogo rozpodіlі kanalіv radiolіnіya nadєtsya dermal telegraph device posіlіvі dоpomogoyu rozpodіlіnіv (Fig. 2.2.1.3).
Fig.2.2.1.3. Bagatocanal system with temporal distribution of canals
For the transmission of radiotelephony alerts, the main amplitude-modulation and frequency-modulation of high-frequency signals are used. Modular low-frequency signal є a large number of signals of different frequencies, mixed in the active smoothness. The width of the spectrum of a standard low-frequency telephone signal is 0.3–3.4 kHz.
In such a rank, a signal is called a physical process, the parameters of which are to remove information (reinforcement) and that is an appendage for processing and transferring to the output.
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 one.
However, sometimes you can manually introduce into the view variegated, or vector signals to the mind.
approved by a number of one-time signals. The integer number N is called the size of such a signal.
Significantly, scho rich signal - the sequence of one-dimensional signals is ordered. For this reason, the direct signals with a different order of directing the components are not equal to one alone.
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 a signal develops at the hour in such a way that the signal value can be muted whether it is the moment or the hour. Signals of this class are usually called analog (continuous). The term "analogue signal" confirms that such a signal is "analogue", similar to the physical process that generates yoga.
A single-mode analog signal is initially represented by its own graph (oscillogram), which can be as interruptless as well as with points.
.
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. Methods of yoga task can be different - mathematical formula, calculation algorithm, nareshti, verbal description.
Analogue (non-interruptible), discrete and digital signals. Often the physical process that generates a signal develops at the hour in such a way that the signal value can be muted whether it is the moment or the hour. Signals of this class are usually called analog (continuous). The term "analogue signal" confirms that such a signal is "analogue", similar to the physical process that generates yoga.
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 victoriously received signals of an off-key analog type. Such signals made it possible to successfully perform some clumsy technical tasks (radio communication, TV broadcasting, then. Bud.). Analogue signals were simply generated, accepted and processed for the help of those available to the roki koshtiv.
Growth was able to reach radio engineering systems, versatility of zastosuvan zmusili shukati new principles їх obudovi. Impulse systems have come to replace the analog clock, the operation of which is based on a variety of discrete signals. The simplest mathematical model of a discrete signal is a numerically anonymous point (- a number) on the clock axis, and a similar signal value is assigned to a skin signal. 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'yavlyayetsya mozhlivist on one and the same radio line to transmit messages from different dzherel, arranging rich-channel zv'yazok s podilom kanaliv for an hour.
It is intuitively clear that analog signals, which change rapidly in hours, require a small amount of time for their sampling.
Let's specialize in a variety of discrete signals - digital signals. Їх is characteristic of those that have significant meanings presented in the form of numbers. From the mirkuvan tekhnіchnіchnіchnіchnіchі zrіchnіzії і іnіzlаіzії і obrobki zvіkorovuyut dvіykovі number z obmezhenіm і, as a rule, nіd nіdno great kіlіkіstyu razryadіv. In the rest of the hour, there was a trend of wide deployment of systems with digital signals. This is due to 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.
Strictly seeming, deterministic signals, like and vidpovidnyh їm deterministic processes, no. Inevitably, the interaction of the system with the nautical physical objects, the presence of chaotic thermal fluctuations and the simple incompetence of knowledge about the system's cob mill - it's all worth looking at real signals like a vipadkovy 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, direct to the dzherelo cosmic vibration, is chaotic colivannia, 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.
The term "signal" is often used in science and technology, and in everyday life. Sometimes, without thinking about the strictness of the terminology, we also understand that signal, alert, information. It’s necessary to call out to the point of incomprehensibility, the “signal” sounds like the Latin term “signum” - “sign”, there is a wide range of meanings. Signals є fіzichnі obi, scho transmit povіdomlennya. Shards of electrical signals are the most effective, their transmission victorious in rich spheres of human activity.
Prote, proceeding to a systematic development of theoretical radio electronics, the next step is to clarify the change in the sense of understanding the “signal”. Apparently, to the accepted tradition, the signal is the process of change at the hour of the physical state of any object, which serves for display, registration, and transmission of remembrance.
Kolo nutrition, which is based on the concepts of "information", "information", is even wider. Wine is an object of sawing respect for engineers, mathematicians, linguists, philosophers.
Proceeding to the discovery of whether there are any objects of existence, the science has to start pragmatically to carry out their previous classification.
Signals can be described with the help of mathematical models. In order to work out the signal of the object of theoretical education and rozrachunkiv, the next designate the method of their mathematical inventory, tobto. 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.
The creation of the model (at the time of the physical signal) is the first step of the systematic cultivation of the quality of the being. Nasampered, the 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 an understandable mathematical model, lies in the fact that we are allowed to describe the power of 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, at the most important vipadkіv, it is important to choose the exact functional fallows, yakі podvіdali b elektrichnymi kolvannyam, scho poserіgayutsya experimentally. To this end, looking at all the variety of information available to you, choose from the prepared 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.
Knowing the mathematical models of signals, you can compare signals among themselves, establish their identity and identity, and classify them.
From the informational point of view, deterministic signals do not interfere with information, but can also serve as handy models for the development of timing and spectral power of signals.
Real signals, to avenge information, act like a vipadkov. But the mathematical models of such signals are supra-symbolically foldable and unmanageable for the development of time-frequency spectral powers of the signals.
Determination of signals is divided into keruyuchi (low-frequency) and radio signals (high-frequency signal). Some signals are sent to the source of information (signals of various sensors) and can be subdivided into periodic and non-periodic. This work is dedicated to modeling clock and spectral powers of periodic signals.
When analyzing periodic signals, the data for systems of orthogonal functions, for example, Walsh, Chebishev, Lugger, sine and cosine and others, became very broad.
The system of basic trigonometric functions - sines and cosines of multiple arguments - is the largest orthogonal system of the nabula. Tse explained by low reasons. First, harmonious colivannya є single function of the hour, which takes its form for the hour of passage through any linear lance(With fixed parameters). The amplitude changes less and that phase of colivannya. In another way, laying out a folding signal for sines and cosines allows you to use the symbolic method, splitting for the analysis of the transmission of harmonic sounds through linear lances. From these, as well as from other reasons, harmonic analysis of wide-width boobs in all the galleries of modern science and technology.
As such a signal of representations in the sight of a sum of harmonic sounds from different frequencies, it seems that it was done spectral layout which signal. Okremі harmonіynі components of the signal to form yogo spectrum. The spectral diagram of a periodic signal is a graphic representation of the coefficients of the Four's low for a particular signal. Separate the amplitude and phase spectral diagrams, tobto. the modules of the arguments of the complex coefficients are low Fur'є, yakі completely signify the structure of the frequency spectrum of the periodic colivannya.
Particularly note the amplitude diagram, as it allows you to judge the percentage difference of quieter harmonics in the spectrum of a periodic signal.
