Analog, discrete and digital signals

One of the trends in the development of modern communication systems is the widespread use of discrete-analog and digital signal processing (DAO and DSP) in them.

The analog signal Z '(t), originally used in radio engineering, can be represented as a continuous graph (Fig. 2.10a). Analog signals include AM, FM, FM signals, telemetry sensor signals, etc. Devices in which analog signals are processed are called analog processing devices. Such devices include frequency converters, various amplifiers, LC filters, etc.

Optimal reception of analog signals, as a rule, provides for an optimal linear filtering algorithm, which is relevant especially when using complex noise-like signals. However, it is in this case that the construction of a matched filter is very difficult. When using matched filters based on multi-tap delay lines (magnetostrictive, quartz, etc.), large attenuation, dimensions and delay instability are obtained. Filters based on surface acoustic waves (SAW) are promising, but the short durations of the signals processed in them and the complexity of tuning the filter parameters limit the scope of their application.

In the 1940s, analog RES were replaced by discrete processing devices for analog input processes. These devices provide discrete analog processing (DAO) of signals and have great capabilities. Here the signal is discrete in time, continuous in states. Such a signal Z '(kT) is a sequence of pulses with amplitudes equal to the values ​​of the analog signal Z' (t) at discrete times t = kT, where k = 0,1,2, ... are integers. The transition from a continuous signal Z '(t) to a pulse train Z' (kT) is called time sampling.

Figure 2.10 Analog, Discrete and Digital Signals

Figure 2.11 Sampling of an analog signal

The sampling of the analog signal in time can be performed by the "AND" coincidence stage (Fig. 2.11), at the input of which the analog signal Z '(t) acts. The coincidence cascade is controlled by the clock voltage UT (t) - short pulses of duration tp, following at intervals T >> tp.

The sampling interval T is selected in accordance with the Kotelnikov theorem T = 1 / 2Fmax, where Fmax is the maximum frequency in the analog signal spectrum. The frequency fd = 1 / T is called the sampling rate, and the set of signal values ​​at 0, T, 2T, ... is a signal with amplitude-pulse modulation (AMM).

Until the late 1950s, PAM signals were used only for converting speech signals. For transmission over the radio relay channel, the AIM signal is converted into a phase-pulse modulation (PPM) signal. In this case, the amplitude of the pulses is constant, and information about the speech message is contained in the deviation (phase) Dt of the pulse relative to a certain average position. Using short pulses of one signal, and placing pulses of other signals between them, multi-channel communication is obtained (but not more than 60 channels).

Currently, DAO is intensively developing on the basis of the use of "fire chains" (PC) and devices with charging connections (CCD).

At the beginning of the 70s, systems with pulse-code modulation (PCM) began to appear on communication networks of various countries and the USSR, where signals in digital form were used.

The PCM process is a conversion of an analog signal into numbers, it consists of three operations: time sampling at intervals T (Fig. 2.10, b), quantization by level (Fig. 2.10, c) and encoding (Fig. 2.10, e). Time sampling is discussed above. The level quantization operation consists in the fact that a sequence of pulses, the amplitudes of which correspond to the values ​​of the analog signal 3 at discrete times, is replaced by a sequence of pulses whose amplitudes can take only a limited number of fixed values. This operation leads to a quantization error (Figure 2.10, d).

Signal ZKV '(kT) is a discrete signal both in time and in states. Possible values ​​u0, u1, ..., uN-1 of the signal Z '(kT) on the receiving side are known, therefore, not the values ​​uk, which the signal received on the interval T, are transmitted, but only its level number k. On the receiving side, according to the received number k, the value uk is restored. In this case, sequences of numbers in the binary number system - code words - are subject to transmission.

The encoding process is to transform the quantized signal Z '(kT) into a sequence of codewords (x (kT)). In fig. 2.10, d depicts code words in the form of a sequence of binary code combinations using three bits.

The considered PCM operations are used in DSP with DSP, while PCM is necessary not only for analog signals, but also for digital ones.

Let's show the need for PCM when receiving digital signals over a radio channel. So, when transmitting in the decameter range, the element xxxxxxxxxxxxxxxxxxxxxxа of the digital signal xi (kT) (i = 0,1), reflecting the n-th code element, the expected signal at the input of the radio receiver together with the additive noise ξ (t) can be represented as:

z / i (t) = μx (kT) + ξ (t), (2.2)

at (0 ≤ t ≥ TE),

where μ is the channel transmission coefficient, TE is the duration of the signal element. From (2.2) it can be seen that the interference at the input of the radio control system forms a set of signals, which are analog oscillations.

Examples of digital circuits are logic gates, registers, flip-flops, counters, memory devices, etc. According to the number of nodes on ICs and LSIs, RFPs with DSP are divided into two groups:

1. Analog-digital RPU, which have separate units implemented on the IC: frequency synthesizer, filters, demodulator, AGC, etc.

2. Digital radio receivers (TsRPU), in which the signal is processed after an analog-to-digital converter (ADC).

In fig. 2.12 shows the elements of the main (information channel) of the DAC of the decameter range: the analog part of the receiving path (AFC), the ADC (consisting of a sampler, a quantizer and an encoder), the digital part of the receiving path (DAC), a digital-to-analog converter (DAC) and a lower filter frequencies (LPF). Double lines indicate the transmission of digital signals (codes), and single lines - analog and PAM signals.

Figure 2.12 Elements of the main (information channel) TsRPU decameter range

AChPT produces preliminary frequency selectivity, significant amplification and conversion of the Z '(T) signal in frequency. The ADC converts the analog signal Z '(T) into a digital signal x (kT) (Fig. 2.10, e).

In CHPT, as a rule, additional frequency conversion, selectivity (in the digital filter - the main selectivity) and digital demodulation of analog and discrete messages (frequency, relative phase and amplitude telegraphy) are performed. At the output of the CChPT, we obtain a digital signal y (kT) (Fig. 2.10, e). This signal, processed according to a given algorithm, from the output of the CHPT enters the DAC or the computer's memory (when receiving data).

In a series-connected DAC and a low-pass filter, the digital signal y (kT) is converted first into a signal y (t), continuous in time and discrete in states, and then in yF (t), which is continuous in time and states (Fig. 2.10, g , h).

Digital filtering and demodulation are the most important of the many methods of digital signal processing in the digital control center. Consider the algorithms and structure of a digital filter (DF) and a digital demodulator (CD).

A digital filter is a discrete system (physical device or computer program). It converts the sequence of numeric samples (x (kT)) of the input signal to the sequence (y (kT)) of the output signal.

The main CF algorithms are: a linear difference equation, a discrete convolution equation, an operator transfer function in the z-plane, and a frequency response.

The equations that describe the sequences of numbers (pulses) at the input and output of the digital filter (discrete system with a delay) are called linear difference equations.

The linear difference equation of the recursive CF has the form:

, (2.3)

where x [(k-m) T] and y [(k-n) T] are the values ​​of the input and output sequences of numeric samples at times (k-m) T and (k-n) T, respectively; m and n - the number of delayed summed previous input and output numeric samples, respectively;

a0, a1,…, am and b1, b2,…, bn are real weight coefficients.

In (3), the first term is a linear difference equation of a nonrecursive CF. The discrete convolution equation of a CF is obtained from a linear difference non-recursive CF by replacing al in it with h (lT):

, (2.4)

where h (lT) is the impulse response of the CF, which is the response to a single impulse.

The operator transfer function is the ratio of the Laplace-transformed functions at the output and input of the CF:

, (2.5)

This function is obtained directly from the difference equations using the discrete Laplace transform and the displacement theorem.

A discrete Laplace transform, for example, a sequence (x (kT)), is understood as obtaining an L - image of the form

, (2.6)

where p = s + jw is the complex Laplace operator.

The theorem of displacement (shift) in relation to discrete functions can be formulated: displacement of the independent variable of the original in time by ± mT corresponds to the multiplication of the L-image by. For example,

Taking into account the linearity properties of the discrete Laplace transform and the displacement theorem, the output sequence of numbers of a non-recursive CF will take the form

, (2.8)

Then the operator transfer function of the non-recursive CF:

, (2.9)

Figure 2.13

Similarly, taking into account formula (2.3), we obtain the operator transfer function of the recursive CF:

, (2.10)

Operator transfer function formulas are complex. Therefore, great difficulties arise in the study of fields and poles (roots of Fig. 2.13 of the polynomial of the numerator and roots of the polynomial of the denominator), which in the p-plane have a periodic structure in frequency.

Analysis and synthesis of CFs is simplified when applying z - transform, when we pass to a new complex variable z related to p by the relation z = epT or z-1 = e-pT. Here the complex plane p = s + jw is displayed by another complex plane z = x + jy. This requires that es + jw = x + jy. In fig. 2.13 shows the complex planes p and z.

Making the change of variables e-pT = z-1 in (2.9) and (2.10), we obtain transfer functions in the z-plane for the non-recursive and recursive CFs, respectively:

, (2.11)

, (2.12)

The transfer function of a non-recursive CF has only zeros, so it is absolutely stable. A recursive CF will be stable if its poles are located inside the unit circle of the z-plane.

The transfer function of the CF in the form of a polynomial in negative powers of the variable z makes it possible to compose a structural diagram of the CF directly from the form of the function HTS (z). The variable z-1 is called the unit delay operator, and in block diagrams it is the delay element. Therefore, the highest powers of the numerator and denominator of the transfer function HTS (z) rivers determine the number of delay elements, respectively, in the non-recursive and recursive parts of the DF.

The frequency response of a digital filter is obtained directly from its transfer function in the z-plane by replacing z with ejl (or z-1 with e-jl) and performing the necessary transformations. Therefore, the frequency response can be written as:

, (2.13)

where KC (l) is the amplitude-frequency (AFC), and φ (l) is the phase-frequency characteristics of the DF; l = 2 f '- digital frequency; f '= f / fD - relative frequency; f is the cyclic frequency.

The characteristic KC (jl) of the DF is a periodic function of the digital frequency l with a period of 2 (or one in relative frequencies). Indeed, ejl ± jn2 = ejl ± jn2 = ejl, since by Euler's formula ejn2 = cosn2 + jsinn2 = 1.

Figure 2.14 Block diagram of the oscillatory circuit

In radio engineering, for analog signal processing, the simplest frequency filter is the LC oscillatory circuit. Let us show that in digital processing the simplest frequency filter is a second-order recursive link, the transfer function of which in the z-plane is

, (2.14)

and the block diagram has the form shown in Fig. 2.14. Here operator Z-1 is a discrete delay element for one clock cycle of the DF, lines with arrows denote multiplication by a0, b2, and b1, “block +” denotes an adder.

To simplify the analysis, in expression (2.14) we take a0 = 1, presenting it in positive powers of z, we obtain

, (2.15)

The transfer function of a digital resonator, as well as an oscillating LC circuit, depends only on the parameters of the circuit. The role of L, C, R is played by the coefficients b1 and b2.

It can be seen from (2.15) that the transfer function of the second-order recursive link has in the z-plane a zero of second multiplicity (at the point z = 0) and two poles

and

The equation for the frequency response of the second-order recursive link is obtained from (2.14), replacing z-1 with e-jl (for a0 = 1):

, (2.16)

The frequency response is equal to the modulus (2.16):

After carrying out elementary transformations. The frequency response of the second-order recursive link will take the form:

Figure 2.15 Graph of a second-order recursive link

In fig. 2.15 shows the graphs in accordance with (2.18) with b1 = 0. It can be seen from the graphs that the second-order recursive link is a narrow-band electoral system, i.e. digital resonator. Shown here is only the working section of the frequency range of the resonator f '<0,5. Далее характери-стики повторяются с интервалом fД

Research shows that the resonant frequency f0 'will take on the following values:

f0 '= fD / 4 when b1 = 0;

f0 ’ 0;

f0 ’> fД / 4 at b1<0.

The values ​​b1 and b2 change both the resonant frequency and the Q-factor of the resonator. If b1 is chosen from the condition

, where, then b1 and b2 will only affect the quality factor (f0 ’= const). The resonator frequency tuning can be provided by changing fD.

Digital demodulator

A digital demodulator is considered in general communication theory as a computing device that processes a mixture of signal and interference.

Let us define the algorithms of the CD when processing analog signals AM and FM with a high signal-to-noise ratio. For this, we represent the complex envelope Z / (t) of a narrow-band analog mixture of signal and interference Z ’(t) at the output of the AChPT in exponential and algebraic form:

and

, (2.20)

is the envelope and full phase of the mixture, and ZC (t) and ZS (t) are the quadrature components.

From (2.20) it can be seen that the envelope of the signal Z (t) contains complete information about the modulation law. Therefore, the digital algorithm for processing the analog AM signal in the CD using the quadrature components XC (kT) and XS (kT) of the digital signal x (kT) has the form:

It is known that the frequency of a signal is the first derivative of its phase, i.e.

, (2.22)

Then from (2.20) and (2.22) it follows:

, (2.23)

Figure 2.16 Block diagram of the CHPT

Using in (2.23) the quadrature components XC (kT) b XS (kT) of the digital signal x (kT) and replacing the derivatives with the first differences, we obtain a digital algorithm for processing the analog FM signal in the CD:

In fig. 2.16 shows a variant of the block diagram of the CChPT when receiving analog signals AM and FM, which consists of a quadrature converter (QC) and a CD.

In the QP, the quadrature components of the complex digital signal are formed by multiplying the signal x (kT) by two sequences (cos (2πf 1 kT)) and (sin (2πf 1 kT)), where f1 is the center frequency of the lowest frequency display of the signal spectrum z '(t ). At the output of the multipliers, digital low-pass filters (LPFs) suppress harmonics with a frequency of 2f1 and extract digital samples of the quadrature components. Here, LPFs are used as a digital basic selectivity filter. The block diagram of the CD corresponds to algorithms (2.21) and (2.24).

The considered algorithms for digital signal processing can be implemented using a hardware method (using specialized computers based on digital ICs, devices with charging connection or devices based on surface acoustic waves) and in the form of computer programs.

In the software implementation of the signal processing algorithm, the computer performs arithmetic operations on the coefficients al, bl and the variables x (kT), y (kT) stored in it.

Previously, the disadvantages of computational methods were: limited performance, the presence of specific errors, the need for resettlement, great complexity and cost. Currently, these limitations are being successfully overcome.

The advantages of digital signal processing devices over analog ones are perfect algorithms associated with training and signal adaptation, ease of control of characteristics, high temporal and temperature stability of parameters, high accuracy and the possibility of simultaneous and independent processing of several signals.

Simple and complex signals. Signal base

The characteristics (parameters) of communication systems improved with the development of the types of signals and their methods of receiving, processing (separation). Each time there was a need for a competent distribution of a limited frequency resource between operating radio stations. Parallel to this, the issue of reducing the emission bandwidth by signals was being addressed. However, there were problems in receiving signals, which were not solved by simple allocation of the frequency resource. Only the use of a statistical method of signal processing - correlation analysis - made it possible to solve these problems.

Simple signals have a signal base

BS = TS * ∆FS≈1, (2.25)

where TS is the signal duration; ∆FS is the spectrum width of a simple signal.

Communication systems operating on simple signals are called narrowband. For complex (composite, noise-like) signals, additional modulation (keying) in frequency or in phase occurs during the duration of the signal TS. Therefore, the following relationship is applied here for the base of a complex signal:

BSS = TS * ∆FSS >> 1, (2.26)

where ∆FSS is the spectrum width of the complex signal.

It is sometimes said that for simple signals ∆FS = 1 / TS is the message spectrum. For complex signals, the signal spectrum expands by ∆FSS / ∆FS times. This results in redundancy in the signal spectrum, which determines the useful properties of complex signals. If, in a communication system with complex signals, the information transmission rate is increased to obtain the duration of the complex signal TS = 1 / ∆FSS, then a simple signal and a narrow-band communication system are formed again. The useful properties of the communication system disappear.

Ways to spread the signal spectrum

The discrete and digital signals discussed above are time division signals.

Let's get acquainted with wideband digital signals and with methods of multiple access with code (in shape) channel division.

Broadband signals were originally used in military and satellite communications because of their useful properties. Here, their high immunity from interference and secrecy were used. The communication system with broadband signals can work when energy interception of the signal is impossible, and eavesdropping without a signal sample and without special equipment is impossible even with a received signal.

Shannon suggested using pieces of white thermal noise as a carrier of information and a method of broadband transmission. He introduced the concept of the bandwidth of a communication channel. He showed the connection between the possibility of error-free transmission of information with a given ratio and the frequency band occupied by the signal.

The first communication system with complex signals from segments of white thermal noise was proposed by Costas. In the Soviet Union, L.E. Varakin suggested using broadband signals when the code division multiple access method is implemented.

For a temporary representation of any variant of a complex signal, you can write the ratio:

where UI (t) and (t) are the envelope and initial phases, which are slowly changing

Functions compared to cosω 0 t; - carrier frequency.

With the frequency representation of the signal, its generalized spectral form has the form

, (2.28)

where are coordinate functions; - expansion coefficients.

Coordinate functions must satisfy the orthogonality condition

, (2.29)

and the expansion coefficients

(2.30)

For parallel complex signals, trigonometric functions of multiple frequencies were initially used as coordinate functions

, (2.31)

when each i-th variant of a complex signal has the form

Z i (t) = t . (2.32)

Then, taking

A ki = and = - arktg (β ki / ki), (2.33)

Ki, βki - coefficients of expansion in the trigonometric Fourier series of the i-th signal;

i = 1,2,3, ..., m; m is the base of the code, we get

Z i (t) = t . (2.34)

Here the signal components occupy frequencies from ki1 / 2π = ki1 / TS to ki2 / 2π = ki2 / TS; ki1 = min (ki1) and ki2 = max (ki2); ki1 and ki2 - numbers of the smallest and largest harmonic components, which significantly affect the formation of the i-th signal variant; Ni = ki2 - ki1 + 1 is the number of harmonic components of the complex i-th signal.

Signal bandwidth

∆FSS = (ki2 - ki1 + 1) ω 0 / 2π = (ki2 - ki1 + 1) / TS. (2.35)

The main part of the signal energy spectrum is concentrated in it.

It follows from relation (35) that the base of this signal

BSS = TS ∙ ∆FSS = (ki2 - ki1 + 1) = Ni, (2.36)

is equal to the number of harmonic components of the signal Ni, which are formed by the i-th version of the signal

Figure 2.17

b)

Figure 2.18 Signal spreading scheme with periodic sequence plot

Since 1996-1997, for commercial purposes, Qualcomm began to use for the formation of parallel complex signals based on (28) a subset (φ k (t)) of full Walsh functions orthogonalized on an interval. At the same time, the method of multiple access with code division of channels is implemented - the CDMA standard (Code Division Multiple Access)

Figure 2.19 Correlation receiver schematic

Useful properties of wideband (composite) signals

Figure 2.20

When communicating with mobile stations (MS), multipath (multipath) signal propagation is manifested. Therefore, signal interference is possible, which leads to the appearance of deep dips (fading of signals) in the spatial distribution of the electromagnetic field. So in urban conditions at the receiving point there can be only reflected signals from high-rise buildings, hills, etc., if there is no line of sight. Therefore, two signals with a frequency of 937.5 MHz (l = 32cm), arriving with a time shift of 0.5 ns with a path difference of 16cm, are added in antiphase.

The signal level at the input of the receiver also changes from the transport passing by the station.

Narrowband communication systems cannot operate in multipath environments. So if at the input of such a system there are three signal beams of one message Si (t) –Si1 (t), Si2 (t), Si3 (t), which overlap in time due to the difference in the length of the path, then they are divided at the output of the strip filter (Yi1 (t), Yi2 (t), Yi3 (t)) is impossible.

Communication systems with complex signals resist the multipath nature of radio propagation. So, choosing the ∆FSS band such that the duration of the folded pulse at the output of the correlation detector or matched filter is less than the delay time of adjacent beams, one can receive one beam or, providing appropriate pulse delays (Gi (t)), add up their energy, which will increase the ratio signal / noise. The American communication system Rake, like a rake, collected the received beams of the signal reflected from the Moon and summarized them.

The principle of signal accumulation can significantly improve the noise immunity and other properties of the signal. The idea of ​​accumulating a signal is given by a simple repetition of the signal.

The first element for this purpose was a frequency selective system (filter).

Correlation analysis allows you to determine the statistical relationship (dependence) between the received signal and the reference signal located on the receiving side. The concept of the correlation function was introduced by Taylor in 1920. The correlation function is a statistical mean of the second order over time, or a spectral mean, or a probabilistic mean.

If time functions (continuous sequences) x (t) and y (t) have arithmetic mean values

With time division of channels;

Code division multiplexing.

The periodic function is:

f (t) = f (t + kT), (2.40)

where T is the period, k is any integer (k =, 2,…). Periodicity exists along the entire time axis (-< t <+ ). При этом на любом отрезке времени равном T будет полное описа­ние сигнала.

Figure 2.10, a, b, c shows a periodic harmonic signal u1 (t) and its spectrum of amplitudes and phases.

Figure 2.11, a, b, c shows the graphs of a periodic signal u2 (t) - a sequence of rectangular pulses and its spectrum of amplitudes and phases.

So, any signals can be represented in the form of a Fourier series for a certain period of time. Then the separation of signals will be represented through the parameters of the signals, i.e. through the amplitudes, frequencies, and phase shifts:

a) signals, the rows of which with arbitrary amplitudes, non-overlapping frequencies and arbitrary phases are separated in frequency;

b) signals, the rows of which with arbitrary amplitudes overlap in frequency, but phase-shifted between the corresponding components of the rows are separated in phase (the phase shift is proportional to the frequency);

The high capacity of communication systems with composite signals will be shown below.

c) signals, the rows of which with arbitrary amplitudes, with components overlapping in frequency (frequencies may coincide) and arbitrary phases are separated in shape.

Shape separation is a code separation when there are complex signals (samples) specially created from simple signals on the transmitting and receiving sides.

Upon reception, a complex signal is first subject to correlation processing, and then

a simple signal is being processed.

Sharing the frequency resource with multiple access

Nowadays, signals can be transmitted in any medium (in the surrounding space, in a wire, in a fiber-optic cable, etc.). To increase the efficiency of the frequency spectrum, and for one and the transmission lines form group channels for transmitting signals over one communication line. On the receiving side, the opposite process takes place - channel separation. Let's consider the methods of channel separation used:

Figure 2.21 Frequency Division Multiple Access FDMA

Figure 2.22 Time Division Multiple Access TDMA.

Figure 2.23 Code Division Multiple Access CDMA

Encryption in wi-fi networks

Data encryption in wireless networks has received so much attention because of the very nature of wireless networks. Data is transmitted wirelessly using radio waves, and in general, omnidirectional antennas are used. Thus, the data is heard by everyone - not only the one to whom it is intended, but also the neighbor who lives behind the wall or "interested" who stops with a laptop under the window. Of course, the distances over which wireless networks operate (no amplifiers or directional antennas) are short - about 100 meters in ideal conditions. Walls, trees, and other obstructions dull the signal a lot, but that still doesn't solve the problem.

Initially, only the SSID (network name) was used for security. But, generally speaking, this method can be called protection with a big stretch - the SSID is transmitted in clear text and no one bothers the attacker to eavesdrop on it, and then substitute the desired one in their settings. Not to mention the fact that (this applies to access points), the broadcast mode can be enabled for the SSID, i.e. it will be forcibly broadcast to all listeners.

Therefore, there was a need for data encryption. The first such standard was WEP - Wired Equivalent Privacy. Encryption is performed using a 40 or 104 bit key (stream encryption using the RC4 algorithm on a static key). And the key itself is a set of ASCII characters with a length of 5 (for a 40-bit) or 13 (for a 104-bit key) characters. The set of these characters is translated into a sequence of hexadecimal digits, which are the key. Drivers from many manufacturers allow hexadecimal values ​​(of the same length) to be entered directly instead of ASCII characters. Please note that the algorithms for translating from an ASCII sequence of characters into hexadecimal key values ​​may differ from manufacturer to manufacturer. Therefore, if your network uses dissimilar wireless equipment and you cannot set up WEP encryption using an ASCII key phrase, try entering the key in hexadecimal instead.

But what about the manufacturers' statements about support for 64 and 128-bit encryption, you ask? That's right, marketing plays a role here - 64 is more than 40, and 128 is 104. In reality, data encryption occurs using a key of length 40 or 104. But besides the ASCII phrase (the static component of the key), there is also such a thing as Initialization Vector - IV Is the initialization vector. It serves to randomize the rest of the key. The vector is randomly selected and dynamically changes during operation. In principle, this is a reasonable solution, since it allows you to introduce a random component into the key. The vector is 24 bits long, so the total key length is 64 (40 + 24) or 128 (104 + 24) bits.

All would be good, but the used encryption algorithm (RC4) is currently not particularly strong - with a strong desire, in a relatively short time, you can brute-force the key. Still, the main vulnerability of WEP is related to the initialization vector. The IV is only 24 bits long. This gives us roughly 16 million combinations - 16 million different vectors. Although the figure "16 million" sounds pretty impressive, everything in the world is relative. In real work, all possible key variants will be used in the interval from ten minutes to several hours (for a 40-bit key). After that, the vectors will start repeating. An attacker only needs to collect a sufficient number of packets by simply listening to the wireless network traffic and find these repeats. After that, the selection of a static c

Let's classify the signals. Signals are divided into:

deterministic;

random.

Deterministic signals are signals that are precisely determined at any time. In contrast, some parameters of random signals cannot be predicted in advance.

Strictly speaking, since the issuance of a particular message by a message source (for example, a sensor) is random, it is impossible to accurately predict the change in the values ​​of the signal parameters. Consequently, the signal is fundamentally random. Deterministic signals have a very limited independent meaning only for the purposes of setting up and adjusting information and computer technology, playing the role of standards.

Depending on the structure of the parameters, signals are subdivided into:

discrete;

continuous;

discrete continuous.

A signal is considered discrete for a given parameter if the number of values ​​that this parameter can take is finite (countable). Otherwise, the signal is considered continuous for this parameter. A signal that is discrete in one parameter and continuous in another is called discrete-continuous.

In accordance with this, the following types of signals are distinguished (Fig. 1.4.):

a) Continuous in level and time (analog) are signals at the output of microphones, temperature sensors, pressure sensors, etc.

b) Continuous in level, but discrete in time. Such signals are obtained by sampling analog signals in time.

Rice. 1.4. Varieties of signals.

By sampling we mean the transformation of a continuous time function (in particular a continuous signal) into a discrete time function representing a sequence of quantities called coordinates, samples or samples (sample value).

The most widespread method is discretization, in which the role of coordinates is played by instantaneous values ​​of a continuous function (signal) taken at certain points in time S (t i), where i = 1,…, n. The time intervals between these moments are called sample intervals. This type of sampling is often referred to as pulse amplitude modulation (PAM).

c) Discrete in level, continuous in time. Such signals are obtained from continuous ones as a result of level quantization.

By level quantization (or simply quantization) is meant the transformation of some quantity with a continuous scale of values ​​(for example, the amplitude of a signal) into a quantity with a discrete scale of values.

This continuous scale of values ​​is divided into 2m + 1 intervals, called quantization steps. Of the set of instantaneous values ​​belonging to the j-th quantization step, only one value S j is allowed, it is called the j-th quantization levels. Quantization is reduced to replacing any instantaneous value of a continuous signal with one of a finite set of quantization levels (usually the closest one):

S j, where j = -m, -m + 1, ..., -1,0,1, ..., m.

The set of S j values ​​forms a discrete scale of quantization levels. If this scale is uniform, i.e. the difference ΔS j = S j - S j-1 is constant, the quantization is called uniform. Otherwise, it will be uneven. Due to the simplicity of technical implementation, uniform quantization has become the most widespread.

d) Discrete in level and time. Such signals are obtained by sampling and quantizing simultaneously. These signals are easy to represent in digital form (digital sample), i.e. in the form of numbers with a finite number of digits, replacing each pulse with a number denoting the number of the quantization level that the pulse reached at a particular time. For this reason, these signals are often referred to as digital signals.

The impetus for the presentation of continuous signals in discrete (digital) form was the need to classify speech signals during World War II. An even greater incentive to digital conversion of continuous signals was the creation of computers, which are used as a source or receiver of signals in many information transmission systems.

Here are some examples of digital conversion of continuous signals. For example, in digital telephone systems (standard G.711), the replacement of an analog signal with a sequence of samples occurs with a frequency of 2F = 8000 Hz, T d = 125 μs. (Since the frequency range of the telephone signal is 300-3400 Hz, and the sampling frequency according to the Nyquist theorem -Kotelnikova should be at least twice the maximum frequency of the converted signal F). Further, each pulse is replaced in an 8-bit analog-to-digital converter (ADC - ADC-Analog-to-Digital Converter) with a binary code that takes into account the sign and amplitude of the sample (256 quantization levels). This quantization process is called Pulse Code Modulation (PCM or PCM). In this case, a non-linear quantization law called "A = 87.6" is used, which better takes into account the nature of human perception of speech signals. The transmission speed of one telephone message turns out to be 8 × 8000 = 64 Kbps. A 30-channel telephone messaging system (the first level of the hierarchy of the CCITT standard - PDH-E1) with time division of channels already operates at a speed of 2048 Kbit / s.

When digital music is recorded on a CD (Compact Disk), containing a maximum of 74 minutes of stereo sound, a sampling frequency of 2F≈44.1 kHz is used (since the hearing limit of the human ear is 20 kHz plus a 10% margin) and 16 bit linear quantization of each sample (65536 audio signal levels, 7-8 bits are enough for speech).

The use of discrete (digital) signals dramatically reduces the likelihood of obtaining distorted information, because:

in this case, efficient coding techniques are applicable that provide error detection and correction (see Topic 6);

it is possible to avoid the effect of accumulation of distortions inherent in a continuous signal during their transmission and processing, since the quantized signal can be easily restored to its original level whenever the amount of accumulated distortion approaches half the quantization step.

In addition, in this case, the processing and storage of information can be carried out by means of computer technology.

Almost from the very moment of inception, human tribes faced the need not only to accumulate information, but also to exchange it with each other. However, if it was not so difficult to do this with neighbors (language and writing), then with those who were at long distances, this process caused some problems.

Over time, they were solved with the invention of the signal. at first they were quite primitive (smoke, sound, etc.), but gradually mankind discovered new laws of nature, which contributed to the invention of new ways to transmit information. Let's find out what types of signals are, and also consider which of them are most often used in modern society.

What is called a signal

This word means information encoded by one system, which is transmitted through a special channel and can be decoded by another system.

Many scientists believe that the ability of biological organisms or even individual cells to interact with each other (signaling the presence of nutrients or danger) has become the main driving force of evolution.

Each physical process can act as a signal, the parameters of which are adapted to the type of transmitted data. For example, in a telephone system, a transmitter converts the speaker's words into an electrical voltage signal, which is transmitted through wires to a receiving device, near which the listening person is located.

Signal and message

These two concepts are very close in meaning - they contain certain data transmitted from the sender to the recipient. However, there is a tangible difference between them.

To achieve this goal, the message must be accepted by the addressee. That is, its life cycle consists of three stages: information coding - transmission - message decoding.

In the case of a signal, its acceptance is not a prerequisite for its existence. That is, the information encrypted in it can be decoded, but whether it will be done by someone is unknown.

Classification according to different criteria of signals: main types

In nature, there are many types of signals with different characteristics. In this regard, various criteria for these phenomena are used to classify them. Thus, there are three categories:

• By feeding method (regular / irregular).
• By the type of physical nature.
• By the type of function that describes the parameters.

Signals by type of physical nature

Depending on the method of education, the types of signals are as follows.

• Electrical (information carrier - time-varying current or voltage in an electrical circuit).
• Magnetic.
• Electromagnetic.
• Thermal.
• Ionizing radiation signals.
• Optical / light.
• Acoustic (sound).

The last two types of signals are also the simplest examples of communication technical operations, the purpose of which is to notify about the peculiarities of the current situation.

Most often they are used to warn of danger or system malfunctions.

Often, sound and optical varieties are used as coordinators for the smooth operation of automated equipment. So some kinds of control signals (commands) are stimulating for the system to take action.

For example, in fire alarms, when smoke traces are detected by the sensors, they emit a shrill sound. That, in turn, is perceived by the system as a control signal to extinguish the fire source.

Another example of how a signal (types of signals by the type of physical nature are listed above) activates the work of the system in case of danger is the thermoregulation of the human body. So, if due to various factors the body temperature rises, the cells "inform" the brain about it, and it turns on the "body cooling system", better known to everyone as sweating.

By function type

Different categories are allocated for this parameter.

• Analog (continuous).
• Quantum.
• Discrete (impulse).
• Digital signal.

All of these types of signals are electrical. This is due to the fact that they are not only easier to handle, but they are also easily transmitted over long distances.

What is an analog signal and its types

This name is given to signals of natural origin that change continuously in time (continuous) and can take on different values ​​over a certain interval.

Due to their properties, they are perfect for data transmission in telephone communications, radio broadcasting, and television.

In fact, all other types of signals (digital, quantum and discrete) are analog converted by nature.

Depending on the continuous spaces and the corresponding physical quantities, different types of analog signals are distinguished.

• Straight.
• Section.
• Circle.
• Spaces characterized by multidimensionality.

Quantized signal

As already mentioned in the last paragraph, this is still the same analog form, but its difference is that it has been quantized. At the same time, its entire range of values ​​was subdivided into levels. Their number is represented in numbers of a given bit width.

Typically, this process is used in practice when compressing audio or optical signals. The more levels of quantization, the more accurate the transformation of the analog form into the quantum one becomes.

The variety in question also belongs to those that arose artificially.

In many classifications of types of signals, this signal is not distinguished. However, it does exist.

Discrete view

This signal is also artificial and has a finite number of levels (values). As a rule, there are two or three of them.

In practice, the difference between discrete and analog signal transmission can be illustrated by comparing sound recording on a vinyl record and a CD. In the first, information is presented in the form of a continuous audio track. But on the second - in the form of laser-burned dots with different reflectivity.

This type of data transmission occurs by converting a continuous analog signal into a set of discrete values ​​in the form of binary codes.

This process is called sampling. Depending on the number of symbols in the code combinations (uniform / uneven), it is divided into two types.

Digital signals

Today this method of information transmission is persistently replacing the analog one. Like the previous two, it is also artificial. In practice, it is represented as a sequence of numerical values.

Unlike analog, the one under consideration transmits data much faster and better, simultaneously clearing them from noise interference. At the same time, this is the weakness of the digital signal (the other types of signals are in the previous three paragraphs). The fact is that information filtered in this way loses "noisy" data particles.

In practice, this means that whole parts disappear from the transmitted image. And when it comes to sound - words or even whole sentences.

In fact, any analog signal can be modulated to digital. To do this, it undergoes two simultaneous processes: sampling and quantization. As a separate method of transmitting information, the digital signal is not divided into types.

Its popularity contributes to the fact that in recent years new generation televisions have been created specifically for digital, rather than analog, image and sound transmission. However, they can be connected to regular TV cables using adapters.

Signal modulation

All of the above methods of data transmission are associated with such a phenomenon as modulation (for digital signals - manipulation). Why is it needed?

As you know, electromagnetic waves (with the help of which different types of signals are transmitted) are prone to attenuation, and this significantly reduces the range of their transmission. To prevent this from happening, low-frequency vibrations are transferred to the region of long high-frequency waves. This phenomenon is called modulation (manipulation).

In addition to increasing the distance of data transmission, thanks to it, the noise immunity of signals is increased. And also it becomes possible to simultaneously organize several independent channels of information transmission at once.

The process itself is as follows. The device, called a modulator, receives two signals simultaneously: low-frequency (carries certain information) and high-frequency (without information, but is capable of being transmitted over long distances). In this device, they are transformed into one, which simultaneously combines the merits of both of them.

The types of output signals depend on the modified parameter of the input carrier high frequency oscillation.

If it is harmonic, this modulation process is called analog.

If it is periodic, it is pulsed.

If the carrier signal is just a direct current, this type is called noise-like.

The first two types of signal modulation, in turn, are divided into subspecies.

Analog modulation is like this.

• Amplitude (AM) - change in the amplitude of the carrier signal.
• Phase (FM) - the phase changes.
• Frequency - only the frequency is affected.

Types of modulation of pulse (discrete) signals.

• Amplitude-pulse (AIM).
• Pulse frequency (PFM).
• Pulse width (PWM).
• Phase-impulse (FIM).

Having considered what methods of data transmission exist, we can conclude that, regardless of their type, they all play an important role in a person's life, helping him to develop comprehensively and protecting him from possible dangers.

With regard to analog and digital signals (with the help of which information is transmitted in the modern world), then, most likely, in the next twenty years in developed countries the former will be almost completely replaced by the latter.

Considering signals and types of signals, it must be said that there are different amounts of these connections. Every day, any person is faced with the use of an electronic device. Without them, modern life is no longer imagined by anyone. We are talking about the work of a TV, radio, computer, and so on. Previously, no one thought about what signal is used in many workable devices. Nowadays, the words analog, digital and discrete have been heard for a long time.

Not all, however, some of the above signals are considered quite high quality and reliable. Digital transmission is not as old as analog transmission. This is due to the fact that technology began to support this type only recently, this type of signal was also discovered relatively recently. Any person constantly encounters discreteness. Speaking about the types of signal processing, it must be remembered that this one is a little intermittent.

If you delve into science, then it should be said that the transfer of information is discrete, which allows you to transfer data and change the time of the environment. Due to the last property, a discrete signal can take any value. At the moment, this indicator is fading into the background, after most of the equipment began to be produced on chips.

Digital and other signals are integral, the components interact with each other 100%. In discreteness, the opposite is true. The fact is that here each detail works independently and is responsible for its functions separately.

Signal

Let's consider the types of communication signals a little later, but now you should get acquainted with what, in principle, the signal itself is. This is a common code that is transmitted over the air by systems. This is a general formulation.

In the field of information and some other technologies, there is a special medium that allows messages to be transmitted. It can be created, but it cannot be accepted. In principle, some systems may accept it, but this is not required. If the signal is to be considered a message, then it is imperative to "catch" it.

This data transfer code can be called a common mathematical function. It describes any change to the available parameters. If we consider radio engineering theory, then it should be said that such options are considered basic. It should be noted that the concept of "noise" is analogous to a signal.

It distorts it, can be superimposed on the already transferred code, and also itself is a function of time. The article will describe below the signals and types of signals, we are talking about discrete, analog and digital. Let's take a quick look at the whole theory on the topic.

Types of signals

There are several types, as well as classifications of existing signals. Let's consider them.

The first type is an electrical signal, there are also optical, electromagnetic and acoustic signals. There are several other similar types, but they are not popular. This classification is based on the physical environment.

According to the method of setting the signal, they are divided into regular and irregular. The first type has an analytical function, as well as a deterministic type of data transfer. Random signals can be formed using some theories from higher mathematics, moreover, they are capable of taking on many values ​​in completely different periods of time.

The types of signal transmission are quite different, it should be noted that signals according to this classification are divided into analog, discrete and digital. Often such signals are used to ensure the operation of electrical devices. In order to deal with each of the options, you need to remember the school physics course and read a little theory.

What is the signal being processed for?

The signal should be processed in order to obtain the information that is encrypted in it. If we consider the types of signal modulation, it should be noted that in terms of amplitude and frequency shift keying this is a rather complex process that must be fully understood. Once the information is received, it can be used in very different ways. In some situations, it is formatted and sent further.

There are also other reasons for signal processing to be noted. It consists in compressing the frequencies that are transmitted, but without damaging all the information. Then it is formatted again and transmitted. This is done at slow speeds. If we talk about analog and digital signals, then special methods are used here. There is filtering, convolution and some other functions. They are needed in order to recover information if the signal has been damaged.

Creation and formatting

Many types of information signals, which we will talk about in the article, must be created and then formatted. To do this, you should have a digital-to-analog converter, as well as an analog-to-digital converter. As a rule, both of them are used in one situation: only in the case of using a technique such as DSP.

In other cases, only the first device will do. In order to create physical analog codes and then reformat them into digital methods, it is necessary to use special devices. This will prevent damage to information as much as possible.

Dynamic range

The range of any kind of analog signal is easy to calculate. It is necessary to use the difference between the higher and lower volume levels, which is shown in decibels.

It should be noted that the information depends entirely on the specifics of its execution. Moreover, we are talking about both music and the conversations of an ordinary person. If we take an announcer who will read the news, then his dynamic range will be no more than 30 decibels. And if you read any work in paints, then this figure rises to 50.

Analog signal

The types of signal presentation are quite different. It should be noted, however, that the analog signal is continuous. If we talk about the shortcomings, then many note the presence of noise, which can, unfortunately, lead to loss of information.

Quite often, a situation arises that it is not clear where the code contains really important information, and where it is just distortion. It is because of this that the analog signal has become less popular, and at the moment it is being replaced by digital technology.

Digital signal

It should be noted that such a signal, like other types of signals, is a data stream, which is described by discrete characteristics.

It should be noted that its amplitude can be repeated. If the above-described analog version is capable of arriving at an endpoint with a huge amount of noise, then the digital one does not allow this. He is able to independently eliminate most of the interference in order to avoid damage to information. It should also be noted that this type transfers information without any semantic load.

Thus, a user can easily send multiple messages through one physical channel. It should be noted that, unlike the types of audio signal, which are the most common at the moment, as well as analog, digital is not divided into several types. He is unique and independent. Represents a binary stream. Now it is quite popular, it is easy to use, as evidenced by the reviews.

Digital signal application

Considering the types of signal transmission, it is necessary to say where the digital version is used. How does it differ from many others in transmission and use? The fact is that, entering the repeater, it is completely regenerated.

When a signal arrives at the equipment, which received noise and interference during transmission, it is immediately formatted. Thanks to this, TV towers can re-form the signal, avoiding the use of noise effect.

Analog communication in this case will be much better, since when receiving information with a large amount of distortion, it can be extracted at least partially. If we talk about the digital version, then this is impossible. If more than 50% of the signal has noise, then we can assume that the information is completely lost.

Many people, discussing cellular communication, and of completely different formats and transmission methods, said that sometimes it is almost impossible to talk. People may not hear words or phrases. This can only happen on a digital line if there is noise.

If we talk about analog communication, then in this case the conversation can be continued further. Due to such problems, repeaters generate a signal always on a new one in order to reduce gaps.

Discrete signal

At the moment, a person uses various dialers or other electronic devices that receive signals. The types of signals are quite diverse, and one of them is discrete. It should be noted that in order for such devices to work, it is necessary to transmit an audio signal. That is why a channel is needed that has a much higher bandwidth than was previously described.

What is the reason for this? The fact is that in order to accurately transmit sound, it is necessary to use a discrete signal. It does not create a wave of sound, but a digital copy of it. Accordingly, the transmission comes from the technology itself. The advantages of such a transfer are that batch sending will be carried out in packets, and the amount of transmitted data will decrease.

Subtleties

In the work of computer technology, there has long been such a concept as discretization. Due to such a signal, information that is fully encoded can be used. It is not continuous, and the data is all collected in blocks. Moreover, the latter are separate particles that are completely complete and do not depend on each other.

Modulation types

Describing the types of signals and signals in general, it is also necessary to talk about modulation. What it is? This is a process of changing several oscillation parameters at once, which are carried out according to a certain law. It should be noted that modulation is divided into digital and pulse, as well as some others.

In turn, many of them are divided separately into several types, and there are quite a few of them. It should be said about the main characteristics of such a concept. For example, due to the types of signal modulation, you can achieve stable transmission, minimal loss, but it should be noted that each of them requires a special linearity amplifier.

1. Basic concepts and definitions. Definition of radio electronics. Definition of radio engineering. Signal concept. Classification analysis of signals. Classification analysis of radio engineering circuits. Classification analysis of radio electronic systems.

Modern radio electronics is a generalized name for a number of fields of science and technology associated with the transmission and transformation of information based on the use and transformation of electromagnetic waves and radio frequency waves; the main areas are:

radio engineering, radio physics and electronics.

The main task of radio engineering is to transmit information over a distance using electromagnetic waves. In a broader sense, modern radio engineering is a field of science and technology associated with the generation, amplification, conversion, processing, storage, transmission and reception of electromagnetic waves in the radio frequency range used to transmit information over a distance. As it follows from this, radio engineering and radio electronics are closely related and often these terms replace each other.

The science that studies the physical foundations of radio engineering is called radiophysics.

1. The concept of a signal.

A signal (from Latin signum - a sign) is a physical process or phenomenon that carries a message about an event, the state of an object, or sends control commands, notifications, etc. Thus, the signal is the material carrier of the message. Any physical process (light, electric field, sound vibrations, etc.) can serve as such a carrier. In electronics, mainly electrical signals are studied and used. Signals as physical processes are observed using various instruments and devices (oscilloscope, voltmeters, receivers). Any model reflects a limited number of the most essential features of a real physical signal. Inessential signal features are ignored to simplify the mathematical description of signals. The general requirement for a mathematical model is the maximum approximation to the real process with the minimum complexity of the model. Functions that describe signals can take real and complex values, so they often talk about real and complex signal models.

Signal classification. According to the predictions of the instant. signal values ​​at any time are separated by:

Deterministic signals, i.e. such signals for which instantaneous values ​​for any moment of time are known and predictable with a probability equal to one;

Random signals, i.e. such signals, the value of which at any moment of time cannot be predicted with a probability equal to one.

All signals carrying information are random, since a completely deterministic signal (known) does not contain information.

The simplest examples of deterministic and random signals are line voltages and noise voltages, respectively (see Figure 2.1).

In turn, random and deterministic signals can be subdivided into continuous or analog signals and discrete signals, which have several varieties. If a signal can be measured (observed) at any time, then it is called analog. Such a signal exists at any time. Discrete signals can be observed and measured in discrete (separate) time intervals limited by the time of occurrence. Discrete signals include pulse signals.

The figure shows two types of pulses. Video impulse and radio impulse. When forming radio pulses, a video pulse is used as a control (modulating) signal, and in this case there is an analytical connection between them:

In this case, it is called the envelope of the radio pulse, and the function is its filling.

Pulses are usually characterized by amplitude A, duration, duration of the rise and fall and, if necessary, the frequency or repetition period.

Impulse signals can be of various types. In particular, a distinction is made between impulse signals called discrete (see Fig. 2.3).

This kind of signals can be represented by a mathematical model in the form of a countable set of function values ​​- where i = 1, 2, 3, ...., k, counted at discrete times. The sampling step of the signal in time and in amplitude is usually a constant value for a given type of signal, i.e. minimum signal gain

Each of the values ​​of the finite set S can be represented in the binary system as a number: - 10101; - 11001; - 10111. Such signals are called digital.

Classification of radio systems and the tasks they solve

According to the functions performed, information radio systems can be divided into the following classes:

information transmission (radio communication, radio broadcasting, television);

extraction of information (radar, radio navigation, radio astronomy, radio measurements, etc.);

destruction of information (radio countermeasures);

control of various processes and objects (unmanned aerial vehicles, etc.);

combined.

In the information transmission system, there is a source of information and its recipient. In a radio system for retrieving information, information as such is not transmitted, but is extracted either from its own signals emitted in the direction of the object under study and reflected from it, or from signals from other radio systems, or from the own radio emission of various objects.

Information destruction radio systems serve to interfere with the normal operation of a competing radio system by emitting an interfering signal, or receiving, deliberately distorting and re-emitting a signal.

In radio control systems, the problem is solved by the object of a command sent from the control panel. Command signals are information for the tracker executing the command.

The main tasks solved by the radio system when receiving information are:

Signal detection in the background of interference.

Distinguishing signals against the background of interference.

Estimation of signal parameters.

Play message.

The simplest solution is the first problem, in which, with the given probabilities of correct detection and false alarm, a decision should be made about the presence of a known signal in the received message. The higher the level of the task, the more complex the receiver circuitry becomes.

2. Energy, power, orthogonality and coherence of signals. Mutual energy of signals (similarity integral). Signal rate concept.