General information about radio signals
When transmitting information over a distance with the help of radio engineering systems, various types of radio engineering (electrical) signals are used. Traditionally radio engineering signals are considered to be any electrical signals related to the radio range. From a mathematical point of view, any radio signal can be represented by some function of time u(t ), which characterizes the change in its instantaneous values of voltage (most often), current or power. According to the mathematical representation, the whole variety of radio engineering signals is usually divided into two main groups: deterministic (regular) and random signals.
deterministic called radio signals, the instantaneous values of which are reliably known at any time, i.e., predictable with a probability equal to one /1/. An example of a deterministic radio engineering signal is a harmonic oscillation. It should be noted that, in fact, a deterministic signal does not carry any information and almost all of its parameters can be transmitted over a radio channel with one or more code values. In other words, deterministic signals (messages) essentially contain no information, and there is no point in transmitting them.
random signals are signals, the instantaneous values of which are not known at any time and cannot be predicted with a probability equal to one /1/. Almost all real random signals, or most of them, are chaotic functions of time.
According to the features of the structure of the temporal representation, all radio signals are divided into continuous and discrete.and by the type of transmitted information: analog and digital.In radio engineering, pulse systems are widely used, the operation of which is based on the use of discrete signals. One of the varieties of discrete signals is digital signal /1/. In it, the discrete values of the signal are replaced by numbers, most often implemented in binary code, which represent high (unit) And low (zero) voltage potential levels.
Functions describing signals can take both real and complex values. Therefore, in radio engineering they talk about real and complex signals. The use of one form or another of the signal description was a matter of mathematical convenience.
Spectrum concept
Direct analysis of the impact of signals of complex shape on radio circuits is very difficult and generally not always possible. Therefore, it makes sense to represent complex signals as the sum of some simple elementary signals. The principle of superposition justifies the possibility of such a representation, stating that in linear circuits the effect of the total signal is equivalent to the sum of the effects of the corresponding signals separately.
Harmonics are often used as elementary signals. This choice has a number of advantages:
a) The expansion into harmonics is implemented quite easily by using the Fourier transform.
b) When a harmonic signal is applied to any linear circuit, its shape does not change (remains harmonic). The frequency of the signal is also stored. Amplitude and phase change, of course; they can be calculated relatively simply using the method of complex amplitudes.
c) In engineering, resonant systems are widely used, which make it possible to experimentally isolate one harmonic from a complex signal.
Representing a signal as a sum of harmonics given by frequency, amplitude and phase is called signal decomposition into a spectrum.
The harmonics included in the signal are specified in trigonometric or imaginary exponential form.
2.1.1.Deterministic and random signals
Deterministic signal is a signal whose instantaneous value at any time can be predicted with a probability equal to one.
An example of a deterministic signal (Fig. 10) can be: sequences of pulses (the shape, amplitude and position in time of which are known), continuous signals with given amplitude-phase relationships.
Methods for setting the MM signal: analytical expression (formula), oscillogram, spectral representation.
An example of an MM deterministic signal.
s(t)=S m Sin(w 0 t+j 0)
random signal- a signal, the instantaneous value of which at any time is not known in advance, but can be predicted with a certain probability less than one.
An example of a random signal (Fig. 11) can be a voltage corresponding to human speech, music; the sequence of radio pulses at the input of the radar receiver; interference, noise.
2.1.2. Signals used in radio electronics
Continuous in magnitude (level) and continuous in time (continuous or analog) signals– take any values s(t) and exist at any moment in a given time interval (Fig. 12).
Continuous in magnitude and discrete in time signals are given for discrete values of time (on a countable set of points), the value of the signal s(t) at these points takes any value in a certain interval along the ordinate axis.
The term "discrete" characterizes the way the signal is set on the time axis (Fig. 13).
Quantized in magnitude and continuous in time signals are given on the entire time axis, but the value s(t) can take only discrete (quantized) values (Fig. 14).
Quantized in magnitude and discrete in time (digital) signals– signal level values are transmitted in digital form (Fig. 15).
2.1.3. Pulse signals
Pulse- an oscillation that exists only within a finite period of time. On fig. 16 and 17 show a video pulse and a radio pulse.
For a trapezoidal video pulse, the following parameters are entered:
A is the amplitude;
t and is the duration of the video pulse;
t f is the duration of the front;
t cf is the duration of the slice.
S p (t) \u003d S in (t) Sin (w 0 t + j 0)
S in (t) - the video pulse is the envelope for the radio pulse.
Sin(w 0 t+j 0) – filling the radio pulse.
2.1.4. Special Signals
Switching function (single function(Fig. 18) or the Heaviside function) describes the process of transition of some physical object from the "zero" to the "single" state, and this transition takes place instantly.
Delta function (Dirac function) is a pulse, the duration of which tends to zero, while the height of the pulse increases indefinitely. It is customary to say that the function is concentrated at this point.
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Signal classification
modulator signal radio spectrum
Radio signals are classified:
According to the physical nature of the information carrier:
electrical;
electromagnetic;
optical;
acoustic, etc.;
By way of setting the signal:
regular (deterministic) given by an analytic function;
irregular (random), taking arbitrary values at any time. To describe such signals, the apparatus of probability theory is used.
Depending on the function that describes the parameters of the signal, analog, discrete, quantized and digital signals are distinguished:
continuous (analogue), described by a continuous function;
discrete, described by the function of readings taken at certain points in time;
quantized by level;
discrete signals, quantized by level (digital).
Signal types
Analog signal:
Most signals are analog in nature, that is, they change continuously in time and can take on any value over a certain interval. Analog signals are described by some mathematical function of time.
Example AC - harmonic signal - s(t) = A cos (w t + c).
Analog signals are used in telephony, radio broadcasting, television. It is impossible to enter such a signal into a computer and process it, since at any time interval it has an infinite number of values, and for an accurate (without error) representation of its value, numbers of infinite bit capacity are required. Therefore, it is necessary to convert the analog signal so that it can be represented by a sequence of numbers of a given bit depth.
Discrete signal:
Discretization of an analog signal is that the signal is represented as a sequence of values taken at discrete times. These values are called counts. Dt is called the sampling interval.
Quantized signal:
During quantization, the entire range of signal values is divided into levels, the number of which must be represented in numbers of a given bit depth. The distance between these levels is called the quantization step D. The number of these levels is N (from 0 to N_1). Each level is assigned a number. Signal samples are compared with quantization levels and a number corresponding to a certain quantization level is selected as a signal. Each quantization level is encoded as a binary number with n bits. The number of quantization levels N and the number of digits n of binary numbers encoding these levels are related by the relation n ? log2(N).
Digital signal:
In order to represent an analog signal as a sequence of numbers of a finite bit capacity, it must first be converted into a discrete signal and then subjected to quantization. Quantization is a special case of discretization, when discretization occurs in the same quantity called a quantum. As a result, the signal will be represented in such a way that the approximate (quantized) value of the signal is known for each given time interval, which can be written as an integer. If you write these integers in binary, you get a sequence of zeros and ones, which will be a digital signal.
As a carrier of messages, high-frequency electromagnetic oscillations (radio waves) of the appropriate range are used, which can propagate over long distances.
The carrier frequency oscillation emitted by the transmitter is characterized by: amplitude, frequency and initial phase. In general, it is presented in the form:
i = I m sin(ω 0 t + Ψ 0),
Where: i is the instantaneous value of the current of the carrier oscillation;
I m is the amplitude of the current of the carrier oscillation;
ω 0 is the angular frequency of the carrier oscillation;
Ψ 0 – the initial phase of the carrier wave.
The primary signals (transmitted message, converted into electrical form) that control the operation of the transmitter can change one of these parameters.
The process of controlling high-frequency current parameters using a primary signal is called modulation (amplitude, frequency, phase). The term “manipulation” is used for telegraphic types of transmission.
In radio communications, radio signals are used to transmit information:
radiotelegraph;
radiotelephone;
phototelegraphic;
telecode;
complex types of signals.
Radio telegraph communication differs: by the method of telegraphy; according to the method of manipulation; on the use of telegraph codes; by way of using the radio channel.
Depending on the method and speed of transmission, radiotelegraph communications are divided into manual and automatic. With manual transmission, manipulation is carried out with a telegraph key using the MORSE code. The transmission speed (for auditory reception) is 60-100 characters per minute.
With automatic transmission, manipulation is carried out by electromechanical devices, and reception is carried out using printing machines. Transmission speed 900–1200 characters per minute.
According to the method of using the radio channel, telegraph transmissions are divided into single-channel and multi-channel.
By the method of manipulation, the most common telegraph signals include signals with amplitude keying (AT - amplitude telegraph - A1), with frequency shift keying (FT and DFT - frequency telegraphy and double frequency telegraphy - F1 and F6), with relative phase shift keying (OFT - phase telegraphy - F9).
For the use of telegraph codes, telegraph systems with the MORSE code are used; start-stop systems with 5 and 6 digit codes and others.
Telegraph signals are a sequence of rectangular pulses (parcels) of the same or different duration. The parcel with the shortest duration is called elementary.
Basic parameters of telegraph signals: telegraphy speed (V); manipulation frequency (F);width of the spectrum (2D f).
telegraphy speed V equal to the number of chips transmitted in one second, measured in bauds. At a telegraphy rate of 1 baud, one chip is transmitted per 1 s.
Keying frequency F numerically equal to half the speed of telegraphy V and is measured in hertz: F=V/2 .
Amplitude-shift keyed telegraph signal has a spectrum (Fig.2.2.1.1), which, in addition to the carrier frequency, contains an infinite number of frequency components located on both sides of it, at intervals equal to the manipulation frequency F. three spectrum components located on either side of the carrier. Thus, the width of the spectrum of the amplitude-shift keyed telegraph RF signal is equal to 6F. The higher the keying frequency, the wider the spectrum of the RF telegraph signal.
Rice. 2.2.1.1. Temporal and spectral representation of the AT signal
At frequency shift keying the current in the antenna does not change in amplitude, but only the frequency changes in accordance with the change in the manipulating signal. The spectrum of the signal FT (DFT) (Fig. 2.2.1.2) is, as it were, the spectrum of two (four) independent amplitude-shift keyed oscillations with their own carrier frequencies. The difference between the frequency of "pressing" and the frequency of "squeezing" is called the frequency spacing, denoted ∆f and can be in the range of 50 - 2000 Hz (most often 400 - 900 Hz). The spectrum width of the FT signal is 2∆f+3F.
Fig.2.2.1.2. Temporal and spectral representation of the chirp signal
To increase the throughput of the radio link, multichannel radiotelegraph systems are used. In them, on one carrier frequency of the radio transmitter, two or more telegraph programs can be transmitted simultaneously. There are systems with frequency division multiplexing of channels, with time division of channels and combined systems.
The simplest two-channel system is the system of double frequency telegraphy (DFT). The signals manipulated in frequency in the DCT system are transmitted by changing the carrier frequency of the transmitter due to the simultaneous effect of the signals of two telegraph devices on it. This uses the fact that the signals of two devices operating simultaneously can have only four combinations of transmitted messages. With this method, at any time, a signal of one frequency is emitted, corresponding to a certain combination of manipulated voltages. The receiving device has a decoder, with the help of which telegraph sendings of constant voltage are formed through two channels. Frequency multiplexing consists in the fact that the frequencies of individual channels are located in different parts of the total frequency range and all channels are transmitted simultaneously.
With time division of channels, the radio link is provided to each telegraph device sequentially with the help of distributors (Fig. 2.2.1.3).
Fig.2.2.1.3. Multi-channel time division system
For the transmission of radiotelephone messages, mainly amplitude-modulated and frequency-modulated high-frequency signals are used. The modulating low-frequency signal is a collection of a large number of signals of different frequencies located in a certain band. The spectrum width of a standard low-frequency telephone signal, as a rule, occupies a band of 0.3-3.4 kHz.
From an informational point of view, signals can be divided into deterministic and random.
Any signal is called deterministic, the instantaneous value of which at any time can be predicted with a probability of one. Examples of deterministic signals are pulses or bursts of pulses whose shape, amplitude and position in time are known, as well as a continuous signal with given amplitude and phase relationships within its spectrum.
Random signals include signals whose instantaneous values are not known in advance and can only be predicted with a certain probability less than one. Such signals are, for example, electrical voltage corresponding to speech, music, a sequence of characters of a telegraph code when transmitting a non-repeating text. Random signals also include a sequence of radio pulses at the input of the radar receiver, when the amplitudes of the pulses and the phases of their high-frequency filling fluctuate due to changes in propagation conditions, the position of the target, and some other reasons. Many other examples of random signals can be given. Essentially, any signal that carries information should be considered random.
The deterministic signals listed above, "fully known", no longer contain information. In what follows, such signals will often be referred to as oscillations.
Along with useful random signals in theory and practice, one has to deal with random interference - noise. The noise level is the main factor limiting the information transfer rate for a given signal.
Rice. 1.2. Signals arbitrary in magnitude and time (a), arbitrary in magnitude and discrete in time (b), quantized in magnitude and continuous in time (c), quantized in magnitude and discrete in time (d)
Therefore, the study of random signals is inseparable from the study of noise. Useful random signals, as well as noise, are often referred to as random fluctuations or random processes.
Further subdivision of signals can be related to their nature: one can speak of a signal as a physical process or as encoded, for example, in a binary code, numbers.
In the first case, a signal is understood as some time-varying electrical quantity (voltage, current, charge, etc.) associated in a certain way with the transmitted message.
In the second case, the same message is contained in a sequence of binary-coded numbers.
The signals generated in radio transmitters and radiated into space, as well as entering the receiving device, where they are amplified and some transformations, are physical processes.
In the previous paragraph, it was indicated that modulated oscillations are used to transmit messages over a distance. In this regard, the signals in the radio channel are often divided into control signals and radio signals; the former are modulating, and the latter are modulated oscillations.
Signal processing in the form of physical processes is carried out using analog electronic circuits (amplifiers, filters, etc.).
The processing of digitally encoded signals is carried out with the help of computer technology.
Shown in Fig. 1.1 and the block diagram of the communication channel described in § 1.2 does not contain indications of the type of signal used to transmit the message and the structure of individual devices.
Meanwhile, the signals from the message source, as well as after the detector (Fig. 1.1) can be both continuous and discrete (digital). In this regard, the signals used in modern radio electronics can be divided into the following classes:
arbitrary in magnitude and continuous in time (Fig. 1.2, a);
arbitrary in magnitude and discrete in time (Fig. 1.2, b);
quantized in magnitude and continuous in time (Fig. 1.2, c);
quantized in magnitude and discrete in time (Fig. 1.2, d).
Signals of the first class (Fig. 1.2, a) are sometimes called analog, since they can be interpreted as electrical models of physical quantities, or continuous, since they are set along the time axis at an uncountable set of points. Taki? sets are called continuum. In this case, along the ordinate axis, the signals can take on any value in a certain interval. Since these signals may have discontinuities, as in Fig. 1.2, a, then, in order to avoid incorrectness in the description, it is better to denote such signals by the term continual.
So, the continuum signal s(t) is a function of the continuous variable t, and the discrete signal s(x) is a function of the discrete variable x, which takes only fixed values. Discrete signals can be created directly by the source of information (for example, discrete sensors in control systems or telemetry) or formed as a result of discretization of continuous signals.
On fig. 1.2, b shows a signal given for discrete values of time t (on a countable set of points); the magnitude of the signal at these points can take on any value in a certain interval along the ordinate axis (as in Fig. 1.2, a). Thus, the term discrete characterizes not the signal itself, but the way it is specified on the time axis.
The signal in fig. 1.2, in is given on the entire time axis, however, its value can only take on discrete values. In such cases, one speaks of a signal quantized by level.
In what follows, the term discrete will be used only in relation to discretization in time; discreteness in terms of level will be denoted by the term quantization.
Quantization is used when representing signals in digital form using digital coding, since levels can be numbered with numbers with a finite number of digits. Therefore, a signal discrete in time and quantized in terms of level (Fig. 1.2, d) will be called digital in the future.
Thus, one can distinguish between continual (Fig. 1.2, a), discrete (Fig. 1.2, b), quantized (Fig. 1.2, c) and digital (Fig. 1.2, d) signals.
Each of these signal classes can be assigned to analog, discrete or digital circuits. The relationship between the type of signal and the type of circuit is shown in the functional diagram (Fig. 1.3).
When processing a continuous signal using an analog circuit, no additional signal conversions are required. When processing a continuum signal using a discrete circuit, two transformations are required: signal sampling in time at the input of the discrete circuit and the inverse transformation, i.e., restoration of the continuum structure of the signal at the output of the discrete circuit.
Rice. 1.3. Types of signal and their corresponding circuits
Finally, when digitally processing a continuous signal, two more additional conversions are required: analog-to-digit, i.e., quantization and digital coding at the input of the digital circuit, and inverse digital-to-analogue conversion, i.e., decoding at the output of the digital circuit.
The signal sampling procedure and especially the analog-to-digital conversion require very high speed of the corresponding electronic devices. These requirements increase with increasing frequency of the continuum signal. Therefore, digital technology has become most widespread in the processing of signals at relatively low frequencies (sound and video frequencies). However, advances in microelectronics contribute to a rapid increase in the upper limit of the processed frequencies.
