Generalized signal characteristic. Signal types: analog, digital, discrete

The signal can be characterized by various parameters. Generally speaking, there are a lot of such parameters, but for problems that have to be solved in practice, only a small number of them are essential. For example, when selecting an instrument for monitoring a process, knowledge of signal variance may be required; if the signal is used for control, its power is essential, and so on. Three main parameters of the signal are considered, which are essential for the transmission of information over the channel. The first important parameter is the signal transmission time. T with... The second characteristic that must be taken into account is the power P with signal transmitted over a channel with a certain level of interference P z... The greater the value P with compared with P z, the less likely it is to receive an erroneous reception. Thus, of interest is the relation P c / P z. It is convenient to use the logarithm of this ratio, called the excess of the signal over the noise:

The third important parameter is the frequency spectrum F x... These three parameters allow you to represent any signal in three-dimensional space with coordinates L, T, F in the form of a parallelepiped with volume T x F x L x... This product is called the signal volume and is denoted by V x

The information channel can also be characterized by three corresponding parameters: the channel usage time T to, bandwidth of frequencies passed by the channel F k, and the dynamic range of the channel D k characterizing its ability to transmit different signal levels.

The magnitude

called the channel capacity.

Undistorted signal transmission is possible only on condition that the volume of the signal "fits" into the channel capacitance.

Consequently, the general condition for matching a signal with an information transmission channel is determined by the relation

However, the ratio expresses a necessary but insufficient condition for matching the signal with the channel. A sufficient condition is agreement on all parameters:

For an information channel, the following terms are used: information input speed, information transfer speed and channel bandwidth.

Under speed of information input (information flow) I (X) understand the average amount of information input from the source of messages into the information channel per unit of time. This characteristic of the message source is determined only by the statistical properties of the messages.

Information transfer rate I (Z, Y) - the average amount of information transmitted over the channel per unit of time. It depends on the statistical properties of the transmitted signal and on the properties of the channel.

Bandwidth C - the highest theoretically achievable information transfer rate for a given channel. This is a channel response and is independent of signal statistics.

In order to make the most efficient use of the information channel, it is necessary to take measures to ensure that the information transfer rate is as close as possible to the channel capacity. At the same time, the speed of information input should not exceed the bandwidth of the channel, otherwise not all information will be transmitted over the channel.

This is the main condition for dynamically reconciling the message source and the information channel.

One of the main issues in the theory of information transmission is to determine the dependence of the information transmission rate and bandwidth on the channel parameters and characteristics of signals and interference. These questions were first deeply investigated by K. Shannon.

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Higher professional education
"Tula State University" Polytechnic Institute Department "Automated machine systems"

Informatics concept
Informatics is a technical science that systematizes the methods of creating, storing, reproducing, processing and transmitting data by computer technology, as well as the principles of fu

History of the development of informatics
The history of the computer is closely linked to human attempts to make it easier to automate large amounts of computation. Even simple arithmetic operations with large numbers are difficult

Worldview economic and legal aspects of information technology
The basic legal document in Russia related to informatics is the Law “On Information, Informatization and Information Protection”. The law addresses the issues of legal regulation of information

Syntactic measure of information
Data volume Vd. in a message is measured by the number of characters (bits) in this message. In different number systems, one digit has a different weight and, accordingly

Semantic measure of information
A thesaurus is a collection of information held by a user or a system. Depending on the relationship between the semantic content of information S and the thesaurus of uses

Algorithmic measure of information
Everyone will agree that the word 0101… .01 is more difficult than the word 00… .0, and the word, where 0 and 1 are chosen from the experiment - tossing a coin (where 0 is a coat of arms, 1 is a lattice), is more difficult than both previous ones.

Quantity and quality of information
Consumer quality indicators: representativeness, meaningfulness, sufficiency; relevance, timeliness, accuracy; reliability,

Information units
In modern computers, we can enter textual information, numerical values, as well as graphic and sound information. The amount of information stored in a computer is measured by it

Information and entropy
Can we introduce a reasonable measure of information? American mathematician and engineer Claude Shannon pondered this question. The result of his reflections was the statistic he published in 1948

Messages and signals
Shannon managed to come up with a surprisingly simple and deep model of information transfer, without which no textbook can now do. He introduced the concepts: message source, transmitter

Entropy
Different messages carry different amounts of information. Let's try to compare the following two questions: 1. In which of the five university courses is the student studying? 2. How pack

Redundancy
Let the source of the message convey a sentence in real language. It turns out that every next character is not completely random, and the likelihood of its occurrence is not completely predetermined among

Sensation
The concepts of entropy (unpredictability) of a message and redundancy (predictability) naturally correspond to intuitive ideas about the measure of information. The more unpredictable the message

Information technology concept
Technology, translated from Greek (techne), means art, craftsmanship, skill, and these are nothing more than processes. A process should be understood as a certain set of actions

New information technology
To date, information technology has gone through several evolutionary stages, the change of which was determined mainly by the development of scientific and technological progress, the emergence of

Information Technology Toolkit
Information technology toolkit - one or more interconnected software products for a certain type of computer, the technology of work in which allows you to achieve

Information technology components
Technological concepts used in the production sphere, such as norm, standard, technological process, technological operation, etc., can also be applied in information

Information technology development
The evolution of information technology is most vividly traced in the processes of storage, transportation and processing of information.

First generation of IT
The first generation (1900-1955) is associated with the technology of punched cards, when data recording was represented on them in the form of binary structures. The prosperity of the IBM company in the period 1915-1960 svyat

Second generation IT
The second generation (programmable recording processing equipment, 1955-1980) was associated with the emergence of magnetic tape technology, each of which could store information of ten thousand

Third generation IT
The third generation (operational databases, 1965-1980) is associated with the introduction of online access to data in an interactive mode, based on the use of database systems with

Fourth generation of IT
The fourth generation (relational databases: client-server architecture, 1980-1995) was an alternative to the low-level interface. The idea behind the relational model is

Fifth generation of IT
The fifth generation (multimedia databases, since 1995) is associated with the transition from traditional storing numbers and symbols, to object-relational, containing data with complex behavior

Basic information technology
As already noted, the concept of information technology cannot be considered separately from the technical (computer) environment, i.e. from basic information technology. App

Subject information technology
Subject technology is understood as a sequence of technological stages for converting primary information into resultant information in a certain subject area, independent

Supporting information technology
Providing information technologies are information processing technologies that can be used as a toolkit in various subject areas to solve various

Functional information technology
Functional information technology forms a finished software product (or part of it) designed to automate tasks in a specific subject area and a given

Information technology properties
Among the distinctive properties of information technologies that are strategically important for the development of society, it seems appropriate to single out the following seven most important

Signal encoding and quantization
Physical signals are continuous functions of time. To convert continuous, in particular, analog signal to digital form, analog-to-digital converters are used.

Characteristics of signals transmitted over the channel
The signal can be characterized by various parameters. There are a lot of such parameters, but for tasks that have to be solved in practice, only a small number of them are essential. On the

Signal modulation
Signals are physical processes whose parameters contain information. In telephone communications, the sounds of conversation are transmitted using electrical signals, in television - from

Types and characteristics of media
If we denote the parameters of the carrier through a1, a2, ..., an, then the carrier as a function of time can be represented as: UН = g (a

Signal spectra
The whole variety of signals used in information systems can be divided into 2 main groups: deterministic and random. A deterministic signal is characterized by

Periodic signals
A function x (t) is called periodic if, for some constant T, the following equality holds: x (t) = x (t + nT), where T is the period of the function, n is

Trigonometric form
Any periodic signal x (t) satisfying the Dirichlet condition (x (t) is bounded, piecewise continuous, has a finite number of extrema during the period), we can

Complex form
Mathematically, it is more convenient to operate with the complex form of the Fourier series. It is obtained by applying the Euler transform

Determination of the error
When expanding periodic functions into the sum of harmonics, in practice, they are often limited to a few first harmonics, and the rest are not taken into account. Approximately representing the function

Non-periodic signals
Any non-periodic signal can be considered as a periodic one, the period of which is equal to ¥. In this regard, the spectral analysis of periodic processes can be

Modulation and coding
5.1. Codes: forward, backward, additional, modified One of the ways to perform a subtraction operation is to replace the sign of the

Direct number code
When encoding with direct n-bit binary code, one bit (usually the most significant one) is reserved for the number sign. The remaining n-1 digits are for significant digits. Signed bit value is 0

Reverse number code
The reverse code is built only for a negative number. The inverse code of a binary number is the inverse image of the number itself, in which all bits of the original number take the inverse (inverse

Additional number code
Additional code is built only for negative numbers. The use of direct code complicates the structure of the computer. In this case, the operation of adding two numbers with different signs must be replaced

Modified number code
When adding numbers less than one with a fixed point, you may get a result in absolute value greater than one, which leads to distortion of the calculation results. Bit overflow

Systematic codes
As already indicated, control functions can be implemented with information redundancy. This possibility appears when using special methods of encoding information. V

Even-odd coding
A simple example of code that detects a single error is a code with a parity bit. Its construction is as follows: a parity bit is added to the original word. If the number of ones in the original word is even, then s

Hamming codes
The codes proposed by the American scientist R. Hamming (Figure 3.3) have the ability not only to detect, but also to correct single errors. These codes are systematic.

Distributed data processing
In the era of centralized use of computers with batch processing of information, computer users preferred to purchase computers on which to solve

Generalized structure of a computer network
Computer networks are the highest form of multi-machine associations. The main differences between a computer network and a multi-machine computing complex: Dimension. In sos

Characteristics of a communication channel without interference
Figure 5.4 - The structure of the channel for transmitting information without interference

Characteristics of noisy information transmission channels
Figure 5.5 - The structure of the channel for transmitting information with interference

Methods for increasing the noise immunity of transmission and reception
The basis of all methods of increasing the noise immunity of information systems is the use of certain differences between a useful signal and interference. Therefore, to combat interference

Modern technical means of data exchange and channel-forming equipment
Various types of communication channels are used to transmit messages in computer networks. The most common are dedicated telephone lines and special channels for digital transmission.

Presentation of information in digital machines (CA)
Codes as a means of secret writing appeared in ancient times. It is known that even the ancient Greek historian Herodotus by the 5th century. BC. gave examples of letters that could only be understood by the addressee. Secret

Information bases for monitoring the operation of digital machines
Algorithms for performing arithmetic operations will provide correct results only if the machine is running smoothly. If any abnormality occurs,

Code immunity
The minimum code distance of a certain code is defined as the minimum Hamming distance between any permitted codewords of that code. The irredundant code m

Parity check method
This is an easy way to spot some of the possible errors. We will use half of the possible code combinations as allowed, namely those that have an even number of ones

Checksum method
The above parity check method can be applied multiple times for various combinations of bits of transmitted codewords - and this will allow not only detecting, but also

Hamming codes
The codes proposed by the American scientist R. Hamming have the ability not only to detect, but also to correct single errors. These codes are systematic. According to the Hamm method

Modulo control
A variety of problems can be solved using a control method based on the properties of comparisons. The methods for controlling arithmetic and logical operations developed on this basis are called control n

Numerical control method
With the numerical control method, the code of a given number is defined as the smallest positive remainder after dividing the number by the selected modulus p: rA = A- (A / p) p

Digital control method
With the digital control method, the control code of the number is formed by dividing the sum of the digits of the number by the selected module:

Selecting a module for monitoring
The advantages of the numerical control method are the fairness of the properties of comparisons for control codes, which makes it easier to control arithmetic operations; advantages of the digital method in possible

Add operation modulo 2
The operation of addition modulo 2 can be expressed in terms of other arithmetic operations, for example. EU

Logical multiplication operation
The operation of logical multiplication of two numbers can be expressed through other arithmetic and logical operations:

Control of arithmetic operations
Arithmetic operations are performed on adders for forward, reverse and complementary codes. Suppose that the image of numbers (operands) are stored in the machine in some code, that is, about

Arithmetic codes
Modulo inspection, discussed earlier, can efficiently detect single errors. However, a single error in one bit can lead to a group of errors in several bits.

DAC and ADC
Conversion between analog and digital values is a basic operation in computing and control systems, since physical parameters such as temperature are moved

Digital logic levels
In the vast majority, neither digital-to-analog nor analog-to-digital converters are almost impossible to use without knowing the type of digital input or output used.

Gate-pulse control output
Most digital-to-analog converters, with the exception of series converters (such as those based on charging capacitors), have a basic circuit that reacts to

Analog signals
Typically, analog-to-digital converters (ADCs) are supplied with signals in the form of voltages. Digital-to-analog converters (DAC) often output signals in the form of a voltage at

D / A Converters
Conversion of digital values into proportional analog values is necessary so that the results of digital calculations can be used and easily understood in analog

Digital to analog conversion
Figure 6.2 shows a block diagram of a DAC that takes a 3-bit signed digital word and converts it to an equivalent voltage. The main

Basic types of DAC
As mentioned earlier, the vast majority of DACs that are currently being marketed are built on two main circuits: a weighted resistor chain and an R-2R type. Both named

DAC with weighted resistors
Weighted resistor converters (Figure 6.3) contain a voltage reference, a set of switches, a set of binary-weighted precision resistors, and an operational amplifier.

DAC with R-2R resistor chain
A DAC with an R -2R resistor chain also contains a voltage reference, a set of switches, and an operational amplifier. However, instead of a set of binary-weighted resistors, they contain

Other types of DAC
DACs generally come with either a fixed internal (or external) or external variable voltage reference (multiplying converters). DAC with fixed source

Analog converters
Essentially analog-to-digital converters either convert an analog input signal (voltage or current) into a frequency or pulse train whose duration is measured

Analog to digital conversion
Figure 6.5 shows a rudimentary analog-to-digital conversion model with a DAC constituting a simple block in a conversion system. Reset pulse is set

Push-pull integrating ADCs
A push-pull integrating ADC, as shown in Figure 6.6, contains an integrator, some control logic, a clock generator, a comparator, and an output counter.

Successive approximation ADC
The main reasons why the successive approximation method is almost universally used in computing systems with information transformation are in the reliability of this

Voltage to frequency converters
Figure 6.9 shows a typical voltage-to-frequency converter. It integrates the analog input signal and feeds it to a comparator. When the comparator changes its state,

Parallel ADCs
Serial-to-parallel and simple-to-parallel converters are mainly used where the highest possible speed is required. Sequential conversion

DAC characteristics
When analyzing tabular data, great care must be taken to find out the conditions under which each parameter is determined, and the parameters are most likely determined differently.

ADC characteristics
The characteristics of an ADC are similar to those of a DAC. In addition, almost everything that has been said about the characteristics of the DAC is also true for the characteristics of the ADC. They are also more typical than mi.

System Compatibility
The list of specifications provided by the manufacturers is only a starting point when choosing the appropriate ADC or DAC. Some System Requirements That Affect You

Transmitter compatibility (interchangeability)
Most ADCs and DACs are not universally compatible physically and some are not electrically compatible. Physically, housings differ in size, with the most widespread

Positional number systems
The number system is a set of techniques and rules for writing numbers in digital signs. The most famous is the decimal number system, in which to write h

Number translation methods
Numbers in different number systems can be represented as follows:

Translation of numbers by division by the base of the new system
The translation of integers is carried out by dividing the new number system by the base q2, of correct fractions - by multiplying by the base q2. Division and multiplication operations are performed n

Tabular translation method
In its simplest form, the tabular method is as follows: there is a table of all numbers from one system with the corresponding equivalents from another system; the task of translation is reduced to finding the appropriate

Representation of real numbers in a computer
To represent real numbers in modern computers, a floating point representation method is adopted. This representation is based on the normalized (exponential

Floating point representation
When representing floating point numbers, part of the cell digits is reserved for recording the order of the number, the rest of the digits for recording the mantissa. One digit in each group is allocated for the image

Floating point representation algorithm
convert a number from P-ary number system to binary; represent a binary number in normalized exponential form; calculate the shifted order of the number; ra

The concept and properties of the algorithm
The theory of algorithms is of great practical importance. The algorithmic type of activity is important not only as a powerful type of human activity, as one of the effective forms of his labor.

Algorithm definition
The word "algorithm" itself comes from algorithmi - the Latin form of spelling the name al-Khorezmi, by which the greatest mathematician from Khorezm was known in medieval Europe (a city in the

Algorithm properties
The above definition of an algorithm cannot be considered strict - it is not entirely clear what a “precise prescription” or “a sequence of actions that ensures the desired result is obtained” is. Algorithm

Rules and requirements for the construction of the algorithm
The first rule is that when constructing an algorithm, first of all, it is necessary to specify a set of objects with which the algorithm will work. Formalized (zak

Types of algorithmic processes
Types of algorithmic processes. An algorithm applied to a computer is a precise prescription, i.e. a set of operations and rules for their alternation, with the help of which, starting with some

John von Neumann's principles
The overwhelming majority of computers are based on the following general principles formulated in 1945 by the American scientist John von Neumann (Figure 8.5). For the first time

Functional and structural organization of the computer
Let's consider the device of a computer using the example of the most common computer system - a personal computer. A personal computer (PC) is called a relatively inexpensive uni

Performing arithmetic operations on fixed and floating point numbers
9.6.1 Codes: forward, backward, complementary. For machine representation of negative numbers, forward, complementary, and backward codes are used.

Addition operation
The operation of adding numbers in forward, backward and two's complement codes is performed on the binary adders of the corresponding code. Direct code binary adder (DS

Multiplication operation
Multiplication of numbers presented in fixed point format is carried out on binary adders of direct, reverse and complementary codes. There are several methods

Division operation
The division of binary numbers, represented in the fixed-point format, represents the successive operations of the algebraic addition of the dividend and divisor, and then the remainder and shift. Division is done

Data files
The definitions of the term "file" as well as the term "operating system" can vary in different sources on computer science and computer engineering. Naibole

File structures
The software part of the file system, determined by its purpose, must contain the following components: Ø means of interacting with user processes, which

Information carriers and technical means for storing data
Storage devices are called drives. Their work is based on different principles (mainly magnetic or optical devices), but they are used for one

Organization of data on devices with direct and sequential access
Data organization refers to the way in which the records of a file are arranged in external memory (on a recording medium). The most widespread are the following two types of file organization

Computer Engineering
A set of technical and mathematical tools (computers, devices, instruments, programs, etc.) used for the mechanization and automation of computational processes and

The oldest calculating instruments
The oldest calculating instrument, which nature itself has placed at the disposal of man, was his own hand. "The concept of number and figure," wrote F. Engels, "is not taken from

Abacus development
The tags and ropes with knots could not satisfy the increasing need for means of calculation due to the development of trade. The development of a written account was hampered by two circumstances.

Logarithms
The term "logarithm" originated from a combination of the Greek words logos - ratio, ratio and arithmos - number. The main properties of the logarithm allow you to replace multiplication, division, in

Blaise Pascal's Adder
In 1640, Blaise Pascal (1623-1662) made an attempt to create a mechanical computing machine. There is an opinion that “Blaise Pascal was prompted to the idea of a calculating machine,

Charles Babbage and his invention
In 1812, Charles Babbage begins to ponder possible ways of calculating tables in machines. Babbage Charles (December 26, 1791, London - October 18, 1871, there f)

Hollerith Tabulator
Armed with pencil and paper or, at best, a summing machine, American statisticians of the 19th century were in dire need of automating the time-consuming, tedious, and

Ts3 car
On the eve of the war, the military departments of all countries were interested in the creation of computers. With the financial support of the German Aviation Research Institute Zuse

General purpose electronic computing machine BESM-6
1. Scope: a universal computer for solving a wide class of problems in science and technology (Figure 11.18 and Figure 11.19). 2. Description of the machine: in the structure of BESM-6 for the first time in

IBM 360
In 1964, IBM announced the creation of six models of the IBM 360 family (System 360), which became the first third-generation computers. Models had a single command system

Altair 8800
In January 1975, the latest issue of Popular Electronics magazine was released, the cover of which featured Figure 11.22 Altair 8800, the heart of which was the latest microprocess

Apple Computers
In 1976, the Apple-1 personal computer appeared (Figure 11.23). It was developed in the mid 70s by Steve Wozniak. At the time, he worked for Hewlett-Packard, in

IBM 5150
On August 12, 1981, IBM released the IBM 5150 personal computer (Figure 11.25). The computer cost a lot of money - $ 1,565 and had only 16 KB of RAM and

Description of the project structure
Any program in Delphi consists of a project file (file with dpr extension) and one or more modules (files with pas extensions). Each of these files describes the software

Description of the module structure
Module structure Modules are program units intended for placing program fragments. With the help of the program code contained in them, all

Description of program elements
Elements of a program Elements of a program are its minimal indivisible parts, which still carry a certain significance for the compiler. Elements include:

Elements of the programming language-alphabet
The Alphabet The Object Pascal alphabet includes letters, numbers, hexadecimal numbers, special characters, spaces, and reserved words. Letters are letters

Elements of the programming language - identifiers, constants, expressions
Identifiers Identifiers in Object Pascal are the names of constants, variables, labels, types, objects, classes, properties, procedures, functions, modules, programs, and a field

Object Pascal Expressions
The main elements from which the executable part of the program is constructed are constants, variables and function calls. Each of these elements is characterized by its own knowledge.

Integer and real arithmetic
An expression consists of operands and operators. Operators are located between operands and denote actions that are performed on the operands. As operands of an expression, you can use

Priority of operations
When evaluating the values of expressions, keep in mind that operators have different precedence. Object Pascal defines the following operations: Ø unary not, @;

Built-in functions. Building complex expressions
In Object Pascal, the basic programming unit is a subroutine. There are two types of subroutines: procedures and functions. Both the procedure and the function are the last

Data types
In mathematics, variables are classified according to some important characteristics. A strict distinction is made between real, complex and logical per

Built-in data types
Any really existing data type, no matter how complex it may seem at first glance, is represented by simple components (basic types), which, as a rule, are always present in the language of pro

Integer types
The range of possible values for integer types depends on their internal representation, which can be one, two, four, or eight bytes. Table 15.1 shows the characteristics of integer t

Number sign representation
Many numeric fields have no sign, for example, subscriber number, memory address. Some numerical fields are always offered positive, for example, payout rate, day of the week, PI value. Friend

Arithmetic overflow
Arithmetic overflow - loss of significant digits when evaluating the value of an expression. If only non-negative values can be stored in a variable (BYTE and WORD types)

Real types. Coprocessor
Unlike ordinal types, the values of which are always compared with a number of integers and, therefore, are represented in the PC absolutely exactly, the values of real types

Text types
Text (character) types are data types that consist of one character. Windows uses ANSI code (named after the institute that developed this code - American National Standa

Boolean type
The Boolean data type named after the 19th century English mathematician J. Boole seems very simple. But a number of interesting points are connected with it. First, to the data of this

Output devices
Output devices include primarily monitors and printers. Monitor is a device for visual display of information (in the form of text, tables, figures, drawings, etc.). &

List of components for input and display of text information
The Delphi Visual Component Library contains many components that allow you to display, enter, and edit text information. Table 16.1 provides a list of them.

Displaying Text in Labels of Label, StaticText, and Panel Components
To display various labels on a form, the components Label, StaticText (which appeared only in Delphi 3) and Panel are mainly used.

Edit and MaskEdit windows
To display text information, and even with the additional ability to scroll long texts, you can also use the Edit and Ma editing windows

Multi-line Memo and RichEdit editing windows
The Memo and RichEdit components are multiline text editing windows. They, like the Edit window, are equipped with many functions.

Integer Input and Display - UpDown and SpinEdit Components
Delphi has specialized components for inputting integers - UpDown and SpinEdit. The UpDown component transforms

List Selectors - ListBox, CheckBox, CheckListBox, and ComboBox
The ListBox and ComboBox components display lists of strings. They differ from each other primarily in that the ListBox is only displayed

InputBox function
An input box is a standard dialog box that appears on the screen as a result of a call to the InputBox function. InputBox function value - string

ShowMessage procedure
You can display a message window using the ShowMessage procedure or the MessageDlg function. ShowMessage procedure

File declaration
A file is a named data structure that is a sequence of data elements of the same type, and the number of elements of the sequence is practically unlimited

File purpose
A file variable declaration specifies only the type of file components. In order for the program to be able to output data to a file or read data from a file, it is necessary to specify specific

Output to file
Direct output to a text file is carried out using the write or writeln instruction. In general terms, these instructions are written as follows.

Opening a file for output
Before outputting to a file, it must be opened. If the program that generates the output file has already been used, then it is possible that the file with the results of the program's work is already on the disk.

File open errors
Attempting to open the file may fail and cause a runtime error. There can be several reasons for the failure to open files. For example, the program will try

Input Devices
Input devices include the following: keyboard, scanner, tablet. A computer keyboard is a device for entering information into a computer and supplying control signals.

Opening a file
Opening a file for input (reading) is performed by calling the Reset procedure, which has one parameter - a file variable. Before calling the Reset procedure with

Reading numbers
It should be understood that the text file contains not numbers, but their images. An action performed by a read or readln statement is actually

Reading lines
In a program, a string variable can be declared with or without a specified length. For example: stroka1: string; stroka2

End of file
Suppose there is some text file on the disk. It is necessary to display the contents of this file in a dialog box. The solution to the problem is quite obvious: you need to open the file, read the first line,

Cycle functions in the program. Loops with pre- and postconditions
Algorithms for solving many problems are cyclical, that is, to achieve a result, a certain sequence of actions must be performed several times. For example, program

FOR loop
The for operator is used if a certain sequence of actions needs to be performed several times, and the number of repetitions is known in advance For example, to calculate the values of a function

BREAK and CONTINUE commands
To terminate the current loop statement immediately, you can use the Break subroutine without parameters (this is a subroutine that plays the role of a statement). For example, when in an array with known r

Nested loops
If a cycle includes one or more cycles, then the one containing other cycles inside it is called external, and the cycle contained in another cycle

Array declaration
An array, like any program variable, must be declared in the variable declaration section before use. In general, the instruction for declaring an array looks like the following about

Array output
Array output is understood as the output to the monitor screen (in the dialog box) of the values of the array elements. If the program needs to display the values of all elements of the array,

Array input
Array input is understood as the process of receiving from the user (or from a file) during the program's operation the values of the array elements. "Frontal" solution to the input problem

Using the StringGrid component
It is convenient to use the StringGrid component to enter an array. The StringGrid component icon is located on the Additional tab (Figure 19.1).

Using the Memo component
In some cases, you can use the Memo component to enter an array. The Memo component allows you to enter text that consists of a sufficiently large number of lines, so it is convenient

Finding the minimum (maximum) element of an array
Let us consider the problem of finding the minimum element of an array using the example of an array of integers. The algorithm for finding the minimum (maximum) element of an array is quite obvious: first

Searching an array for a given element
When solving many problems, it becomes necessary to determine whether an array contains certain information or not. For example, check if the surname Petrov is on the list of students. Ass

Errors when using arrays
When using arrays, the most common error is that the value of the subscript expression exceeds the allowed limits specified when declaring the array. If in ka

Bibliographic list
1. Fundamentals of Informatics: Textbook. manual for universities / A.N. Morozevich, N.N. Govyadinova, V.G. Levashenko and others; Ed. A.N. Morozevich. - Minsk: New knowledge, 2001. - 544p., Ill.

Subject index
"Abacus", 167 array, 276 Break, 272 CD-ROM, 161 const, 298 Continue, 273

PAGE 24

ROSTOV TECHNOLOGICAL INSTITUTE

SERVICE AND TOURISM

________________________________________________________________

Department of Radio Electronics

Lazarenko S.V.

LECTURE No. 1

in the discipline "Radio circuits and signals"

Rostov-on-Don

2010

LECTURE 1

INTRODUCTION MAIN CHARACTERISTICS OF SIGNALS

By discipline RADIO CIRCUITS AND SIGNALS

Time: 2 hours

Issues under study: 1. Subject, purpose and objectives of the course

2. Course overview, links to other disciplines

3. A brief history of the development of the discipline

4. General methodology for working on the course, types of classes,

reporting forms, educational literature

5 Signal energy characteristics

6 Correlation characteristics of deterministic signals

7 Geometric methods in signal theory

8 Orthogonal signal theory. Generalized Fourier series

In this lecture, the following elements of the qualification characteristic are implemented:

The student should know the basic laws, principles and methods of analyzing electrical circuits, as well as methods for modeling electrical circuits, circuits and devices.

The student must master the techniques for performing circuit calculations in steady state and transient modes.

1. SUBJECT AND OBJECTIVES OF THE COURSE

The subject of the discipline RADIO ENGINEERING CIRCUITS AND SIGNALS is electromagnetic processes in linear and nonlinear radio engineering circuits, methods for calculating circuits in steady-state and transient modes, continuous and discrete signals and their characteristics.

Discipline takes objects of research from practice - typical circuits and signals from physics - her laws of the electromagnetic field, from mathematics - research apparatus.

The purpose of studying the discipline is to instill in students the skill of calculating the simplest radio engineering circuits and familiarize them with modern algorithms for optimal signal processing.

As a result of studying the discipline, each student must

HAVE A REPRESENTATION:

On modern algorithms for optimal signal processing;

Trends in the development of the theory of radio circuits and signals,

KNOW:

Classification of radio engineering signals;

Time and spectral characteristics of deterministic signals;

Random signals, their characteristics, correlation and spectral analysis of random signals;

Discrete signals and their characteristics;

Digital signal processing algorithms,

BE ABLE TO USE:

Methods for analytical and numerical solution of problems of signal transmission through linear and nonlinear circuits;

Methods for spectral and correlation analysis of deterministic and random signals,

OWN:

Methods for measuring the main parameters and characteristics of radio circuits and signals;

Techniques for analyzing the passage of signals through circuits,

HAVE EXPERIENCE:

Investigations of the passage of deterministic signals through linear stationary circuits, nonlinear and parametric circuits;

Calculation of the simplest radio engineering circuits.

The operational orientation of training in the discipline is ensured by conducting a laboratory workshop, during which each student is taught practical skills:

Work with electrical and radio measuring devices;

Conducting an express analysis of emergency situations in the operation of fragments of radio engineering circuits based on the measurement results.

2 BRIEF OVERVIEW OF THE COURSE, RELATIONSHIP WITH OTHER DISCIPLINES

The discipline "Radio circuits and signals" is based on knowledge and yah "Mathematics", "Physics", "Informatics", and provides the assimilation of art at dents of general scientific and special disciplines, "Metrology and radioism e rhenium "," Devices for generating and forming radio signals "," Devices for receiving and processing signals "," Fundamentals of television and video O technology "," Statistical theory of radio engineering systems "," Radio engineering and systems ", course and diploma project tirovanie.

Studying the discipline "Radio circuits and signals" develops engineering thinking in students, prepares them for mastering special disciplines.

The teaching of the discipline is aimed at:

For a deep study by students of the basic laws, principles and methods of analyzing electrical circuits, the physical essence of electromagnetic processes in electronic devices;

To instill solid skills in the analysis of steady-state and transient processes in circuits, as well as in conducting experiments in order to determine the characteristics and parameters of electrical circuits.

The discipline consists of 5 sections:

1 Signals;

2 Passing signals through linear circuits;

3 Non-linear and parametric circuits;

4 Feedback and self-oscillating circuits

5 Principles of digital signal filtering

3. BRIEF HISTORY OF THE DISCIPLINE DEVELOPMENT

The emergence of the theory of electrical and radio engineering circuits is inextricably linked with practice: with the formation of electrical engineering, radio engineering and radio electronics. Many domestic and foreign scientists have contributed to the development of these areas and their theory.

The phenomena of electricity and magnetism have been known to man for a long time. However, in the second half of the eighteenth century, they began to be studied seriously, haloes of mystery and supernaturalism began to break from them.

Already Mikhail Vasilievich Lomonosov (1711 - 1765) assumed that in nature there is one electricity and that electrical and magnetic phenomena are organically linked. Russian academician Frans Epinus made a great contribution to the science of electricity (1724 - 1802).

The rapid development of the doctrine of electromagnetic phenomena occurred in XIX century, caused by the intensive development of machine production. At this time, humanity invents for its practical needs TELEGRAPH, TELEPHONE, ELECTRIC LIGHTING, METAL WELDING, ELECTRIC GENERATORS and ELECTRIC MOTORS.

Let us indicate in chronological sequence the most striking stages in the development of the theory of electromagnetism.

In 1785 year French physicist Charles Pendant Answer (1736 - 1806) established the law of mechanical interaction of electric charges (Coulomb's law).

In 1819 year Danish Oersted Hans Christian (1777 - 1851) discovered the action of an electric current on a magnetic needle, and in 1820 year French physicist Ampere André Marie (1775 - 1836) established a quantitative measure (force) acting from the side of the magnetic field on the section of the conductor (Ampere's law).

In 1827 year German physicist Om Georg Simon (1787 - 1854) experimentally obtained the relationship between tone and voltage for a section of a metal conductor (Ohm's law).

In 1831 English physicist Michael Faraday (1791 - 1867) established the law of electromagnetic induction, and in 1832 Russian physicist Emiliy Khristianovich Lenz (1804 - 1865) formulated the principle of generality and reversibility of electrical and magnetic phenomena.

In 1873 year on the basis of a generalization of experimental data on electricity and magnetism, the English scientist J.C. Maxwell put forward a hypothesis for the existence of electromagnetic waves and developed a theory to describe them.

In 1888 year German physicist Hertz Heinrich Rudolph (1857 - 1894) experimentally proved the existence of radiation of electromagnetic waves.

The practical use of radio waves was first carried out by the Russian scientist Alexander Stepanovich Popov(1859 - 1905), which May 7, 1895 demonstrated at the meeting of the Russian physicist - chemical society transmitter (spark device) and receiver of electromagnetic waves (lightning detector) .

Late XIX centuries in Russia, famous engineers and scientists worked Lodygin Alexander Nikolaevich (1847 - 1923), who created the world's first incandescent lamp (1873); Yablochkov Pavel Nikolaevich (1847 - 1894), developed the electric candle (1876); Dolivo-Dobrovolsky Mikhail Osipovich (1861 - 1919), created a three-phase system of currents (1889) and the founder of modern energy.

In the XIX century, the analysis of electrical circuits was one of the tasks of electrical engineering. Electric circuits were studied and calculated according to purely physical laws describing their behavior under the influence of electric charges, voltages and currents. These physical laws formed the basis of the theory of electrical and radio engineering circuits.

In 1893 - 1894 years, the works of C. Steinmetz and A. Kennelly developed the so-called symbolic method, which was first applied for mechanical oscillations in physics, and then transferred to electrical engineering, where complex quantities began to be used for a generalized presentation of the amplitude-phase picture of a steady sinusoidal oscillation.

Based on the work of Hertz(1888), and then Pupina (1892) by resonance and tuning RLC circuits and coupled oscillatory systems, problems have arisen in determining the transfer characteristics of the chains.

In 1889 year A. Kennelly developed formally - a mathematical method for the equivalent transformation of electrical circuits.

In the second half XIX century Maxwell and Helmholtz developed methods of loop currents and nodal voltages (potentials), which formed the basis of matrix and topological methods of analysis in later times. Very important was Helmholtz's definition of the principle of SUPERPOSITION, i.e. separate consideration of several simple processes in the same circuit with the subsequent algebraic summation of these processes into a more complex electrical phenomenon in the same circuit. The superposition method made it possible to theoretically solve a wide range of problems that were previously considered insoluble and amenable only to empirical consideration.

The next significant step in the formation of the theory of electrical and radio engineering circuits was the introduction to 1899 year of the concept of complex resistance of an electrical circuit to alternating current.

An important stage in the formation of the theory of electrical and radio engineering circuits was the study of the frequency characteristics of circuits. The first ideas in this direction are also associated with the name of Helmholtz, who used the principle of superposition and the method of harmonic analysis for analysis, i.e. applied the expansion of the function in a Fourier series.

Late XIX century, the concepts of T- and U-shaped circuits were introduced (they began to be called four-poles). Almost at the same time, the concept of electrical filters came into being.

The foundation of the modern theory of radio engineering circuits and radio engineering in general was laid by our compatriots M.B. Shuleikin, B.A. Vedensky, A.I. Berg, A.L. Mints, V.A. Kotelnikov, A.N. Mandelshtamm, N.D. .Papaleksi and many others.

4 GENERAL METHODS OF WORKING ON THE COURSE, TYPES OF LESSONS, REPORTING FORMS, EDUCATIONAL LITERATURE

The study of the discipline is carried out in lectures, laboratory and practical classes.

Lectures are one of the most important types of training and with O provide the basis for theoretical learning. They provide a systematic basis for scientific knowledge in the discipline, focus on teaching e on the most complex and key issues, stimulate their active cognitive activity, form creative thinking.

In lectures, along with the fundamentality, the necessary and May the degree of practical training orientation. The presentation of the material is linked to military practice, specific objects of special equipment, in which electrical circuits are used.

Laboratory exercises are aimed at teaching students the methods of ec With experimental and scientific research, to instill the skills of scientific analysis and generalization of the results obtained, skills in working with laboratory O mining, instrumentation and computing x no one.

In preparation for laboratory classes, students independently or (if necessary) at targeted consultations study the appropriate Yu theoretical material, the general procedure for conducting research, draw up report forms (draw a diagram of the laboratory installation, the necessary tables).

The experiment is the main part of the laboratory work and real and is carried out by each student independently in accordance with the manual for laboratory work. Before carrying out the experiment, a n a survey in the form of a flyer, the purpose of which is to check the quality of O training students for laboratory work. At the same time, it is necessary to pay attention to the knowledge of the theoretical material, the procedure for performing the work, the nature of the expected results. When accepting reports, you should take into account a To accuracy of registration, student compliance with the requirements of ESKD, cash and chie and correctness of the necessary conclusions.

Practical exercises are conducted with the aim of developing skills in solving e nii tasks, the production of calculations. Their main content is right To the technical work of each student. The backside is taken out for practical training a chi having an applied nature. Raising the level of computer software d cooking is carried out in practical training by performing calculations e with the help of programmable microcalculators or personal computers. At the beginning of each lesson, a quiz is conducted, the purpose of the cat O rogo - checking the readiness of students for the lesson, and also - activating a tion of their cognitive activity.

In the process of mastering the content of the discipline among students, the system and methodological skills and skills of independent work are formed. Students are taught the ability to correctly ask a question, put a O the most important task, to report on the essence of the work done, to use before With Coy and visual aids.

To instill primary skills in the preparation and conduct of training sessions, it is envisaged to attract students as assistants to the head of laboratory classes.

Among the most important areas of enhancing the cognitive de I am Problem learning is related to the student body. To implement it with O problem situations for the course as a whole, for individual topics and for O requests that are being implemented:

By introducing new problematic concepts showing how historically they appeared and how they are applied;

By colliding the student with the contradictions between new phenomena e niyas and old concepts;

With the need to choose the right information;

Using the contradictions between the available knowledge on p e the results of the solution and the requirements of practice;

Presentation of facts and phenomena that are inexplicable at first glance with

using well-known laws;

By identifying intersubject connections and connections between phenomena.

In the process of studying the discipline, control of the assimilation of the material is provided in all practical types of classes in the form of briefings, and on topics 1 and 2 in the form of a two-hour test.

To determine the quality of education in general for the discipline, conduct T Xia exam. Students who have completed all the requirements of the curriculum, who have reported on all laboratory work are allowed to the exam, get v shih positive marks on the course work. Exams are held in a mustache T form with the necessary written explanations on the chalkboard (formulas, graphs, etc.). Each student is given a time of no more than 30 minutes to prepare. To prepare for the answer, students can use O to give methodological and reference materials permitted by the head of the department e rials. Preparation for the answer can be carried out in writing. The head of the department can exempt from passing the exam students who have shown T personal knowledge based on the results of current control, with an assessment n ki "excellent".

Thus, the discipline "Radio circuits and signals" is I am is a system of concentrated and at the same time quite complete and a perfect knowledge that allows a radio engineer to freely navigate in the most important issues of operation of special radio technical devices and systems.

BASIC EDUCATIONAL LITERATURE:

1. S. I. Baskakov Radio engineering circuits and signals. 3rd edition. M .: Higher school, 2000.

ADDITIONAL LITERATURE

2. S. I. BASKAKOV Radio engineering circuits and signals. Guide to solving problems: Textbook. manual for radio engineering. specialist. universities. - 2nd edition. M .: Higher school o la, 2002.

3. Popov V.P. Fundamentals of circuit theory. Textbook. for universities.-3rd ed. M .: Higher school about la, 2000.

5 ENERGY CHARACTERISTICS OF THE SIGNAL

The main energy characteristics of a real signal are:

1) instantaneous power, defined as the square of the instantaneous value of a signal

If - voltage or current, then is the instantaneous power released on the resistance and 1 ohm.

Instantaneous power is not additive, i.e. the instantaneous power of the sum of signals is not equal to the sum of their instantaneous powers:

2) the energy over the time interval is expressed as an integral of the instantaneous power

3) the average power in an interval is determined by the value of the signal energy in this interval, referred to a unit of time

where.

If the signal is given for an infinite time interval, then the average power is determined as follows:

Information transmission systems are designed so that information is transmitted with less distortion than specified at a minimum energy and signal power.

The energy and power of the signals, determined at an arbitrary time interval, can be additive if the signals in this time interval are orthogonal. Consider two signals and, which are set on the time interval. The energy and power of the sum of these signals are expressed as follows:

, (1)

. (2)

Here, and, - energy and power of the first and second signals, mutual energy and mutual power of these signals (or the energy and power of their interaction). If the conditions are met

then the signals and over the time interval are called orthogonal, and the expressions(1) and (2) take the form

The concept of orthogonality of signals is necessarily associated with the interval of their determination.

In relation to complex signals, the concepts of instantaneous power, energy and average power are also used. These values are introduced so that the energy characteristics of the complex signal are real values.

1. Instantaneous power is determined by the product of the complex signalto a complex conjugate signal

2. Signal energyover the time interval is, by definition, equal to

3. Signal strengthon the interval is defined as

Two complex signals and, given at a time interval, are orthogonal if their mutual power (or energy) is zero.

6 CORRELATION CHARACTERISTICS OF DETERMINED SIGNALS

One of the most important time characteristics of a signal is the autocorrelation function (ACF), which makes it possible to judge the degree of connection (correlation) of a signal with its time-shifted copy.

For a real signal specified in the time intervaland limited in energy, the correlation function is determined by the following expression:

, (3)

where - the amount of time shift of the signal.

For each value, the autocorrelation function is expressed by some numerical value.

From (3) it follows that the ACF is an even function of the time shift. Indeed, replacing in (3) variable on, we get

When the similarity of the signal with its unshifted copy is the greatest and the functionreaches a maximum value equal to the total signal energy

With an increase, the function of all signals, except for periodic ones, decreases (not necessarily monotonously), and with a relative shift of the signals and by an amount exceeding the signal duration, it vanishes.

The autocorrelation function of a periodic signal is itself a periodic function with the same period.

To assess the degree of similarity of the two signals, the cross correlation function (CCF) is used, which is determined by the expression

Here and - signals given on an infinite time intervaland possessing finite energy.

The value does not change if, instead of delaying the signal, we consider the advance of the first signal.

The autocorrelation function is a special case of the CCF, when the signals and are the same.

In contrast to the function, in the general case, it is not even relative and can reach a maximum of any three.

The value determines the mutual energy of the signals and

7 GEOMETRIC METHODS IN THE THEORY OF SIGNALS

When solving many theoretical and applied problems of radio engineering, the following questions arise: 1) in what sense can we talk about the magnitude of the signal, arguing, for example, that one signal is significantly superior to the other; 2) Is it possible to objectively assess how similar two dissimilar signals are to each other?

In XX v. functional analysis was created a branch of mathematics that summarizes our intuitive ideas about the geometric structure of space. It turned out that the ideas of functional analysis make it possible to create a coherent theory of signals, which is based on the concept of a signal as a vector in a specially constructed infinite-dimensional space.

Linear signal space. Let -many signals. The reason for combining these objects the presence of some properties common to all elements of the set.

The study of the properties of signals that form such sets becomes especially fruitful when it is possible to express some elements of the set through other elements. It is customary to say that many signals are endowed with a certain structure. The choice of this or that structure should be dictated by physical considerations. So, as applied to electrical vibrations, it is known that they can be added, as well as multiplied by an arbitrary scale factor. This makes it possible to introduce the structure of linear space in sets of signals.

The set of signals forms a real linear space if the following axioms are true:

1. Any signal for any takes only real values.

2. For any and there is their sum, and it is also contained in. The summation operation is commutative: and associative:.

3. For any signal and any real number, the signal is defined=.

4. The set M contains a special zero element, such that  is for everyone.

If the mathematical models of signals take complex values, then, assuming in the axiom 3 multiplication by a complex number, we arrive at the concept of a complex linear space.

The introduction of the structure of linear space is the first step towards a geometric interpretation of signals. Elements of linear spaces are often called vectors, emphasizing the analogy between the properties of these objects and ordinary three-dimensional vectors.

The restrictions imposed by the axioms of linear space are very strict. Not every set of signals turns out to be a linear space.

Coordinate basis concept. As in ordinary three-dimensional space, in the linear space of signals, a special subset can be distinguished, which plays the role of coordinate axes.

They say that the set of vectors (}, belonging, is linearly independent if the equality

is possible only if all numerical coefficients vanish simultaneously.

The system of linearly independent vectors forms a coordinate basis in linear space. If the decomposition of some signal is given in the form

then the numbers () are the projections of the signal relative to the selected basis.

In problems of signal theory, the number of basis vectors, as a rule, is infinitely large. Such linear spaces are called infinite-dimensional. Naturally, the theory of these spaces cannot be embedded in the formal scheme of linear algebra, where the number of basis vectors is always finite.

Normalized linear space. Signal energy. In order to continue and deepen the geometric interpretation of the theory of signals, it is necessary to introduce a new concept, which in its meaning corresponds to the length of the vector. This will allow not only to give an exact meaning to the statement of the form "the first signal is greater than the second", but also to indicate how much greater it is.

The length of a vector in mathematics is called its norm. The linear space of signals is normalized if each vector is uniquely associated with the number the norm of this vector, and the following axioms of the normed space are satisfied:

1. The norm is non-negative, i.e.. Norm if and only if .

2. Equality is true for any number.

3. If and are two vectors from , then the triangle inequality holds:.

It is possible to suggest different ways of introducing the rate of signals. In radio engineering, it is most often believed that real analog signals have the norm

(4)

(of the two possible values of the root, a positive one is chosen). For complex signals, the norm

where * - the symbol of the complex conjugate value. The square of the norm is called the signal energy

It is this energy that is released in a resistor with a resistance 1 Ohm, if there is voltage across its terminals.

Determine the signal rate using the formula (4) advisable for the following reasons:

1. In radio engineering, the magnitude of a signal is often judged on the basis of the total energy effect, for example, the amount of heat released in a resistor.

2. The energy norm turns out to be "insensitive" to changes in the signal shape, perhaps significant, but occurring over short periods of time.

Linear normed space with a finite value of the norm of the form (1.15) is called the space of functions with an integrable square and is briefly denoted.

8 THEORY OF ORTHOGONAL SIGNALS. GENERALIZED FOURIER SERIES

Having introduced the structure of a linear space in the set of signals, having determined the norm and metric, we, nevertheless, are deprived of the opportunity to calculate such a characteristic as the angle between two vectors. This can be done by formulating the important concept of the scalar product of elements of a linear space.

Dot product of signals. Recall that if two vectors and are known in an ordinary three-dimensional space, then the square of the modulus of their sum

where is the dot product of these vectors, depending on the angle between them.

Acting by analogy, we calculate the energy of the sum of two signals and:

. (5)

Unlike the signals themselves, their energies are non-additive - the energy of the total signal contains the so-called mutual energy

. (6)

Comparing formulas(5) and (6), define the scalar product of real signals and:

The dot product has the properties:

, where is a real number;

A linear space with such a scalar product, complete in the sense that it contains all the limit points of any converging sequences of vectors from this space, is called a real Hilbert space.

The fundamental Cauchy inequality- Bunyakovsky

If the signals take complex values, then the complex Hilbert space can be defined by introducing the dot product into it by the formula

such that.

Orthogonal signals and generalized Fourier series. Two signals are called orthogonal if their dot product, and hence the mutual energy, is zero:

Let - Hilbert space of signals with a finite energy value. These signals are defined over a period of time, finite or infinite. Suppose that an infinite system of functions is given on the same segment, orthogonal to each other and having unit norms:

They say that in this case an orthonormal basis is specified in the signal space.

Let's expand an arbitrary signal in a row:

(7)

Performance (7) is called the generalized Fourier series of the signal in the selected basis.

The coefficients of this series are found as follows. Take a basic function with an arbitrary number, multiply both sides of the equality (7) and then integrate the results over time:

. (8)

Since the basis is orthonormal on the right-hand side of the equality (8) only a member of the sum with a number will remain, therefore

The possibility of representing signals by means of generalized Fourier series is a fact of great fundamental importance. Instead of studying the functional dependence in an uncountable set of points, we get the opportunity to characterize these signals with a countable (but, generally speaking, infinite) system of coefficients of a generalized Fourier series.

The energy of the signal, represented in the form of a generalized Fourier series. Consider some signal expanded in a series in the orthonormal basis system:

and calculate its energy by directly substituting this series into the corresponding integral:

(9)

Since the basis system of functions is orthonormal, the sum (9) only members with numbers will be nonzero. This gives us a wonderful result:

The meaning of this formula is as follows: the signal energy is the sum of the energies of all components from which the generalized Fourier series is composed.

Senior Lecturer of the Department of Radio Electronics S. Lazarenko

When studying the generalized theory of signals, the following issues are considered.

1. Basic characteristics and methods of analysis of signals used in radio engineering for information transmission.

2. The main types of signal transformations in the process of building channels.

3. Methods of construction and methods of analysis of radio engineering circuits by means of which operations are performed on the signal.

Radio signals can be defined as signals that are used in radio engineering. According to their purpose, radio technical signals are divided into signals:

radio broadcasting,

television,

telegraph,

radar,

radio navigation,

telemetry, etc.

All radio signals are modulated. When forming modulated signals, primary signals of low frequency (analog, discrete, digital) are used.

Analog signal repeats the law of changing the transmitted message.

Discrete signal - the source of the message transmits information at certain time intervals (for example, about the weather), in addition, a discrete source can be obtained as a result of sampling in time of an analog signal.

Digital signal Is a display of a message in digital form. Example: a text message is encoded into a digital signal.

All message characters can be encoded in binary, hexadecimal and other codes. Coding is carried out automatically using an encoder. Thus, the code symbols are converted to standard signals.

The advantage of digital data transmission is high noise immunity. The reverse conversion is carried out using a digital-to-analog converter.

Mathematical models of signals

When studying the general properties of signals, one usually distracts from their physical nature and purpose, replacing them with a mathematical model.

Mathematical model - the chosen method of mathematical description of the signal, reflecting the most essential properties of the signal. On the basis of a mathematical model, it is possible to classify signals in order to determine their general properties and fundamental differences.

Radio signals are usually divided into two classes:

deterministic signals,

random signals.

Deterministic signal Is a signal, the value of which at any time is a known value or can be calculated in advance.

Random signal Is a signal, the instantaneous value of which is a random variable (for example, a sound signal).

Mathematical models of deterministic signals

Deterministic signals are divided into two classes:

periodic,

non-periodic.

Let s ( t ) - deterministic signal. Periodic signals are described by a periodic function of time:

and are repeated through the period T ... Approximately t >> T ... The rest of the signals are non-periodic.

A pulse is a signal whose value differs from zero for a limited time interval (pulse width ).

However, when describing a mathematical model, functions are used that are specified on an infinite time interval. The concept of effective (practical) pulse duration is introduced:

Exponential momentum.

For example: determining the effective duration of an exponential pulse as the time interval during which the signal value decreases by 10 times. Determine the effective pulse width for the drawing:

Signal energy characteristics . Instantaneous power is the signal power across 1 ohm:

For a non-periodic signal, we introduce the concept of energy at a resistance of 1 Ohm:

For a periodic signal, the concept of average power is introduced:

The dynamic range of a signal is defined as the ratio of the maximum P ( t ) to that minimum P ( t ) , which allows you to provide a given transmission quality (usually expressed in dB):

Calm speech of the announcer has a dynamic range of about 25 ... 30 dB, for a symphony orchestra up to 90 dB. Selecting a value P min associated with the level of interference:
.

The magnitude

called the channel capacity.

Undistorted signal transmission is possible only on condition that the volume of the signal "fits" into the channel capacitance.

Consequently, the general condition for matching a signal with an information transmission channel is determined by the relation

However, the ratio expresses a necessary but insufficient condition for matching the signal with the channel. A sufficient condition is agreement on all parameters:

For an information channel, the following terms are used: information input speed, information transfer speed and channel bandwidth.

Bandwidth C - the highest theoretically achievable information transfer rate for a given channel. This is a channel response and is independent of signal statistics.

This is the main condition for dynamically reconciling the message source and the information channel.

As noted above, the transmitted signals are unambiguously associated with the transmitted messages. The mathematical description of a signal is some function of time s(t). Communication signals can be classified according to several criteria.

In message theory, signals are primarily divided into deterministic (regular) and random. The signal is called deterministic, if it can be described by a known function of time. Therefore, a deterministic signal is understood as a signal that corresponds to a known transmitted message and which can be accurately predicted in advance for an arbitrarily long period of time. Deterministic signals are usually subdivided into periodic, almost periodic and non-periodic.

In real conditions, the signal at the receiving point is unknown in advance and cannot be described by a definite function of time. The received signals are unpredictable, random due to several reasons. First, because a regular signal cannot carry information. Indeed, if everything was known about the transmitted signal, then there would be no need to transmit it. Usually, on the receiving side, only some parameters signal. Secondly, the signals are random in nature due to various kinds of interference, both external (space, atmospheric, industrial, etc.) and internal (noises of lamps, resistances, etc.). The received signal is also distorted due to passing through the communication line, the parameters of which are often a random function of time.

Communication signal model is not one function of time s(t) , but a set of some functions that represent a random process. Each specific signal is one of realizations a random process that can be described by a deterministic function of time. Often, the recipient knows the ensemble of possible messages (signals). The task is to determine which message from a given ensemble was transmitted from the adopted implementation of the signal mixture with interference.

Thus, the transmitted signal must be considered as a set of functions that are implementations of a random process. The statistical characteristics of this process fully describe the properties of the signal. However, the solution of many specific problems becomes difficult in this case. Therefore, the study of signals and their passage through various circuits is advisable to begin with individual implementations as deterministic functions.

A complete description of the signal is not always necessary. Sometimes a few generalized characteristics are enough for analysis, which most fully reflect the properties of the signal. One of the most important characteristics of a signal is its durationT, which determines the required time for the channel and is simply related to the amount of information transmitted by this signal. The second characteristic is spectrum width signal F, which characterizes the behavior of the signal during its duration, the rate of its change. As a third characteristic, one could introduce one that would determine the amplitude of the signal throughout its existence, for example, power. However, the signal strength RWith in itself does not determine the conditions for its transmission over real communication channels with interference. Therefore, the signal is usually characterized by the ratio of signal power and interference:

which is called signal-to-noise ratio or signal-to-noise ratio.

A signal characteristic called dynamic range,

which determines the interval of changes in signal levels (for example, loudness during transmission of a telephone message) and imposes corresponding requirements on the linearity of the path. From this side, the signal can be characterized by the so-called peak factor

representing the ratio of the maximum signal value to the effective one. The greater the peak factor of the signal, the worse the energy performance of the radio device will be.

From the point of view of the transformations performed on messages, it is customary to divide signals into video signals (unmodulated) and radio signals (modulated). Usually the video signal spectrum is concentrated in the low frequency region. When using modulation, the video signal is called modulating. The spectrum of the radio signal is concentrated around a certain middle frequency in the high frequency region. Radio signals can be transmitted in the form of electromagnetic waves.

In conclusion of the section, we briefly describe the signals used in various types of communication. In fig. 1.2 shows a video signal in the form of a continuous pulse train. Such a signal is generated for telegraphic types of work using a five-digit binary code. The bandwidth used for the transmission of such signals depends on the telegraphy speed and is, for example, 150-200 Hz when using the ST-35 telegraph apparatus and transmitting 50 characters per second. When transmitting telephone messages, the signal is a continuous f
function times, as shown in fig. 1.2 b.

V
commercial telephony, the signal is usually transmitted in the frequency range from 300 Hz to 3400 Hz. Broadcasting requires a bandwidth of approximately 40 Hz to 10 kHz for high-quality speech and music transmission. When transmitting still images using a phototelegraph, the signal has the form shown in Fig. 1.Z a.

It is a step function. The number of possible levels is equal to the number of volumes and semitones transmitted. One or more standard telephone channels are used for transmission. When transmitting moving pictures in television using 625 decomposition lines, a frequency bandwidth of 50 Hz to 6 MHz is required. In this case, the signal has a complex discrete-continuous structure. The modulated signals have the form shown in Fig. 1.3 b (with amplitude modulation).