Material carriers of information are signals of various physical natures. In a narrow sense, signals are oscillations. electric current, stress, electromagnetic waves, mechanical vibrations of some elastic medium. Information signals are formed by changing certain parameters of the carrier according to a certain law. Thus, an information signal can be any physical process whose parameters can change depending on the transmitted information. This process of changing media parameters is usually called modulation, and the parameters themselves informational. Unlike a message, reception of a signal after it is generated is not mandatory.

As a signal passes through the physical environment, it is affected by various destabilizing factors, resulting in noise and interference of various natures (Fig. 12.4). When recording a signal, the main task is to isolate the useful component from the general signal and maximum suppression of noise and interference.

Rice. 12.3.

Rice. 12.4.

To analyze, explore and process signals you must use mathematical model signal, which is a mathematical description of the signal. The word "model" comes from the Latin modelium, which means: measure, method, image. The purpose of the model is that it displays only the most important features of the signal and allows one to abstract from its physical nature and the material form of the carrier. As a rule, the signal description is given functional dependence its values ​​on the independent variable, for example, s(t).

The simplest signals are one-dimensional signals, that is signal value depends on one parameter (for example, sound signals). An example of a one-dimensional signal in Figures 12.3, 12.4.

Rice. 12.5.

In the general case, signals are multidimensional functions of spatial, temporal and other coordinates. An example is the intensity of a computer image p(x,y) (Fig. 12.5).

According to the form of presentation, signals are of two types - analog and digital (discrete)(Fig. 12.6). Analog signal is defined for any value of the independent parameter, that is, it is a continuous function of a continuous argument. Sources of analog signals, as a rule, are physical processes and phenomena that are continuous in their development (the dynamics of changes in the values ​​of certain properties) in time, in space or in any other independent variable, while the recorded signal is similar (analogous) to the process generating it.

Rice. 12.6.

The fundamental analog signal is a sine wave (Fig. 12.7). In general, a sinusoidal signal can be represented as follows:

A sinusoidal signal can be defined by three parameters: maximum amplitude, frequency and phase. The maximum amplitude is called maximum value or signal intensity over time; The maximum amplitude is measured, usually in volts. Frequency is the rate at which signals repeat (in cycles per second, or hertz). An equivalent parameter is the signal period T, which is the time during which the signal repeats; hence, . Phase is a measure of the relative time shift within a particular signal period.

Rice. 12.7.

Most analog signals in nature have a more complex form. Periodic, that is, signals of arbitrary shape that repeat after a certain time interval, can be represented as a sum of harmonic oscillations using the Fourier transform. By applying the Fourier transform, i.e. By adding together a sufficient number of sinusoidal signals with appropriate amplitudes, frequencies and phases, an electromagnetic signal of any shape can be obtained. Similarly, any signal is considered as a collection of periodic analog (sinusoidal) signals with different amplitudes, frequencies and phases.

A digital signal can be expressed as follows:

The totality of the spectral components of the signal forms it range. The amplitude of each spectral component characterizes the energy of the corresponding harmonic of the fundamental frequency of the signal. The higher the rate of change of the signal, the more high-frequency harmonics there are in its spectrum. The difference between the maximum and minimum frequencies in the signal spectrum is called signal spectrum width.

In accordance with the change in the amplitude of the analog signal, its power or energy changes, proportional to the square of the amplitude. Depending on the time of signal measurement, there are average and instantaneous power. The decimal logarithm of the ratio of the maximum instantaneous signal power to the minimum is called dynamic range signal.

A sign of a protected signal that allows it to be detected and recognized among other signals is called unmasking. Signal attributes describe the parameters of fields and electrical signals generated by the protected object: power, frequency, type of signal, spectrum width, etc.

Analog signal is described by a set of parameters that are its characteristics. These include the parameters we discussed earlier:

• frequency and frequency range;
• amplitude (and power) of the signal;
• signal phase;
• signal duration;
• type of modulation;
• signal spectrum width;
• dynamic range of the signal.

The unmasking features of signals can also include the time of their appearance, depending on which the signals are divided into regular (the time of appearance is known to the recipient) and random (the time of appearance is unknown).

The type of information contained in the signal changes its unmasking features. For example, a standard speech signal transmitted over telephone line, has a spectrum width of 300-3400 Hz, audio - 16-20000 Hz, television - 6-8 MHz, etc.

For discrete signals, the amplitude has a finite, predetermined set of values. The most common signal used, in particular, in computers, is a binary signal. A binary signal has two amplitude levels: low and high.

A discrete signal is generally characterized by the following parameters: amplitude, power, pulse duration, period, signal spectrum width, pulse duty cycle (the ratio of the period to the duration of one pulse).

A binary periodic signal is characterized by the following parameters:

When discrete signals pass through wires, their spectrum changes due to various external influencing factors and the properties of the transmission medium. As a result, their shape is distorted and the steepness of the pulses decreases, which reduces their transmission range.

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1. Analog and discrete signals

1. A signal that continuously changes over time so that its value can be measured at any time is called analog.

2. A signal that varies discretely in time so that its values ​​are determined only at countable (with a certain step) moments in time is usually called discrete.

3. In discrete-time circuits (with discrete signals), the input and output always have a common wire connected to ground. That's why they don't show it.

4. Conversions: analog signal to discrete signal are carried out using a sampler key and a low-pass filter.

5. Discrete signals are characterized by the speed of transmission of discrete values.

A signal in the form of samples is called amplitude pulse modulated.

The sample rate is the same as the sampling rate.

2. Discrete and digital signals

1. Digital (binary) signals are a special case of discrete ones, when for the amplitude of any pulse only two values ​​are allowed: “0” or “1”, respectively, current and non-current signals.

2. Transitions from discrete signal to digital signal are carried out using a digital-to-analog converter (DAC) and an analog-to-digital converter (ADC).

3. The ADC converts in two steps:

each discrete signal value is converted from decimal to binary system calculus;

A binary number is associated with a binary signal having two positions “0” and “1”.

5 = 12 2 + 02 1 + 12 0 101

4. Digital signals are characterized by their transmission speed in bits/sec.

A bit is a minimal message indicating the choice of one of two values: “0” and “1”.

1 byte is equal to 8 bits.

5. Transmission through the LEC of 1 bit/s usually requires 1 Hz of frequency bandwidth.

3. The concept of time division of channels

1. A circuit that has several inputs and outputs and is characterized by a functional purpose (amplifier, filter, etc.) is called a system.

2. The system of time division of channels is based on giving each subscriber his own individual operating time.

3. A. Individual operating time means the presence of individual sampling keys.

B. Digital signals are transmitted through the line.

CU is a key management device.

B. For switching, incoming and outgoing lines of subscribers are connected to the PBX.

With spatial switching, the numbers of incoming and outgoing lines are the same, with time switching they are different.

The memory is a delaying (several intervals) device.

4. Digital filter and its elements

1. In discrete signals, information is carried by the pulse envelope x(n), which depends on the sample number n.

2. Operations on the pulse envelope are carried out using a device called a digital filter.

3. The digital filter is implemented by computer technology and consists of three elements:

signal filter analog discrete

4. Digital filter synthesis consists of three stages:

A. An analog device is found that performs the desired operation on the signal envelope.

B. Impulse response analog device is sampled as a sequence of pulses with an envelope g(n).

B. A digital filter is implemented as a model.

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Signals are information codes that people use to convey messages to information system. The signal can be given, but it is not necessary to receive it. Whereas a message can only be considered a signal (or a set of signals) that was received and decoded by the recipient (analog and digital signal).

One of the first methods of transmitting information without the participation of people or other living beings were signal fires. When danger arose, fires were lit sequentially from one post to another. Next, we will consider the method of transmitting information using electromagnetic signals and will dwell in detail on the topic analog and digital signal.

Any signal can be represented as a function that describes changes in its characteristics. This representation is convenient for studying radio engineering devices and systems. In addition to the signal in radio engineering, there is also noise, which is its alternative. No noise useful information and distorts the signal by interacting with it.

The concept itself makes it possible to escape from specific physical quantities when considering phenomena related to the encoding and decoding of information. The mathematical model of the signal in research allows one to rely on the parameters of the time function.

Signal types

Signals based on the physical environment of the information carrier are divided into electrical, optical, acoustic and electromagnetic.

According to the setting method, the signal can be regular or irregular. A regular signal is represented as a deterministic function of time. An irregular signal in radio engineering is represented by a chaotic function of time and is analyzed by a probabilistic approach.

Signals, depending on the function that describes their parameters, can be analog or discrete. A discrete signal that has been quantized is called a digital signal.

Signal Processing

Analog and digital signals are processed and directed to transmit and receive information encoded in the signal. Once information is extracted, it can be used for various purposes. In special cases, information is formatted.

Analog signals are amplified, filtered, modulated, and demodulated. Digital data can also be subject to compression, detection, etc.

Analog signal

Our senses perceive all information entering them in analog form. For example, if we see a car passing by, we see its movement continuously. If our brain could receive information about its position once every 10 seconds, people would constantly get run over. But we can estimate distance much faster and this distance is clearly defined at each moment of time.

Absolutely the same thing happens with other information, we can evaluate the volume at any moment, feel the pressure our fingers exert on objects, etc. In other words, almost all information that can arise in nature is analogue. The easiest way to transmit such information is through analog signals, which are continuous and defined at any time.

To understand what analog looks like electrical signal, you can imagine a graph that displays amplitude on the vertical axis and time on the horizontal axis. If we, for example, measure the change in temperature, then a continuous line will appear on the graph, displaying its value at each moment in time. To transmit such a signal using electric current, we need to compare the temperature value with the voltage value. So, for example, 35.342 degrees Celsius can be encoded as a voltage of 3.5342 V.

Analog signals used to be used in all types of communications. To avoid interference, such a signal must be amplified. The higher the noise level, that is, interference, the more the signal must be amplified so that it can be received without distortion. This method of signal processing spends a lot of energy generating heat. In this case, the amplified signal may itself cause interference for other communication channels.

Nowadays, analog signals are still used in television and radio, to convert the input signal in microphones. But in general, this type of signal is being replaced or replaced by digital signals everywhere.

Digital signal

A digital signal is represented by a sequence of digital values. The most commonly used signals today are binary digital signals, as they are used in binary electronics and are easier to encode.

Unlike the previous signal type, a digital signal has two values ​​“1” and “0”. If we remember our example with temperature measurement, then the signal will be generated differently. If the voltage supplied by the analog signal corresponds to the value of the measured temperature, then a certain number of voltage pulses will be supplied in the digital signal for each temperature value. The voltage pulse itself will be equal to “1”, and the absence of voltage will be “0”. The receiving equipment will decode the pulses and restore the original data.

Having imagined what a digital signal will look like on a graph, we will see that the transition from zero to maximum is abrupt. It is this feature that allows the receiving equipment to “see” the signal more clearly. If any interference occurs, it is easier for the receiver to decode the signal than with analog transmission.

However, it is impossible to restore a digital signal with a very high noise level, while it is still possible to “extract” information from an analog type with large distortion. This is due to the cliff effect. The essence of the effect is that digital signals can be transmitted over certain distances, and then simply stop. This effect occurs everywhere and is solved by simply regenerating the signal. Where the signal breaks, you need to insert a repeater or reduce the length of the communication line. The repeater does not amplify the signal, but recognizes its original form and produces an exact copy of it and can be used in any way in the circuit. Such signal repetition methods are actively used in network technologies.

Besides everything else digital systems What distinguishes it from analogue ones is the ability to encode and encrypt information. This is one of the reasons for the transition of mobile communications to digital.

Analog and digital signal and digital-to-analog conversion

We need to talk a little more about how analog information is transmitted over digital communication channels. Let's use examples again. As already mentioned, sound is an analog signal.

What's happening in mobile phones that transmit information via digital channels?

Sound entering the microphone undergoes analog-to-digital conversion (ADC). This process consists of 3 steps. Individual signal values ​​are taken at equal intervals of time, a process called sampling. According to Kotelnikov’s theorem on channel capacity, the frequency of taking these values ​​should be twice as high as the highest signal frequency. That is, if our channel has a frequency limit of 4 kHz, then the sampling frequency will be 8 kHz. Next, all selected signal values ​​are rounded or, in other words, quantized. How more levels will be created, the higher the accuracy of the reconstructed signal at the receiver. All values ​​are then converted into binary code, which is transmitted to the base station and then reaches the other party, which is the receiver. A digital-to-analog conversion (DAC) procedure takes place in the receiver's phone. This is a reverse procedure, the goal of which is to obtain a signal at the output that is as identical as possible to the original one. Next, the analog signal comes out in the form of sound from the phone speaker.

There are four types of signals s(t): continuous continuous time, continuous discrete time, discrete continuous time and discrete discrete time.

Continuous-time signals are called continuous-time (analog) signals for short. They can change at arbitrary moments, taking on any of a continuous set of possible values ​​(Fig. 1.3). Such signals include the well-known sinusoid.

Rice. 1.3 Continuous signal

Rice. 1.4 Continuous discrete time signal

Continuous discrete-time signals can take arbitrary values, but change only at certain, predetermined (discrete) moments (Fig. 1.4).

Discrete continuous-time signals differ in that they can change at arbitrary moments, but their values ​​take only allowed (discrete) values ​​(Fig. 1.5).

Discrete time signals (abbreviated discrete) (Fig. 1.6) at discrete times can only take on allowed (non-crete) values.

The signals generated at the output of the discrete message-to-signal converter are, as a rule, discrete in terms of the information parameter, i.e., they are described by a discrete time function and a finite set of possible values. In data transmission technology, such signals are called digital data signals (DDS). The data signal parameter, the change of which reflects a change in the message, is called representing (information). In Fig. Figure 1.7 shows a DSD, the representing parameter of which is amplitude, and the set of possible values ​​of the representing parameter is equal to two. Part of a digital data signal that differs from the other parts in the value of one of its representing ones. parameters is called the DAC element.

The fixed value of the state of the representing parameter of the signal is called the significant position. The moment at which the significant position of the signal changes is called significant (SM).

Rice. 1.5 Discrete continuous time signal

Rice. 1.6 Discrete signal

Rice. 1.7 Digital data signal

The time interval between two adjacent significant moments of the signal is called significant (SI)

The minimum time interval, which is equal to the significant time intervals of the signal, is called unit ( intervals a-b, b-c and others in Fig. 1 7). A signal element having a duration equal to a unit time interval is called a unit element (e e)

The term unit element is one of the main ones in data transmission technology. In telegraphy it corresponds to the term elementary parcel

There are isochronous and anisochronous data signals. For an isochronous signal, any significant time interval is equal to a unit interval or an integer. Anisochronous signals are signals whose elements can have any duration, but not less than. Another feature of anisochronous signals is that they can be separated from each other in time at an arbitrary distance

3. Signals. Types of signals and their parameters

Characteristics of various signals

All signals can be divided into periodic And non-periodic.

A signal is called periodic, the values ​​of which are repeated at certain equal intervals of time, called the signal repetition period, or simply period. For a non-periodic signal this condition is not satisfied.

The simplest periodic signal is a harmonic oscillation.

Where S, w – amplitude and angular frequency of vibration.

Another example of a periodic signal is a sequence of rectangular pulses (Fig. 3.2, A). What do you think this sequence of impulses consists of? It turns out that they are made from sinusoids. Take a look at fig. 3.2. As an initial sinusoid, we choose one whose oscillation period coincides with the period T rectangular pulses (Fig. 3.2, b)

, (3.1)

where is the amplitude of the sinusoid, and .

Oscillation (3.2.) of a given frequency and amplitude can be represented as a graph: mark the value on the frequency axis and draw a vertical line with a height equal to the signal amplitude (see Fig. 3.2, b).

The next sinusoid has an oscillation frequency 3 times greater and an amplitude 3 times less.

The sum of these two sinusoids still bears little resemblance to rectangular pulses (Fig. 3.2, V). But if we add sinusoids to them with oscillation frequencies of 5, 7, 9, 11, etc.

times larger, and with amplitudes of 5, 7, 9, 11, etc. times smaller, then the sum of all these oscillations:

Rice. 3.2. Periodic sequence of rectangular pulses (a) and the formation of its signal (b–e) where , will not be so different from rectangular pulses (Fig. 3.2, And G d

). Thus, the degree of “squareness” of the pulses is determined by how many sinusoids with increasingly higher oscillation frequencies we will sum up.