Let's classify the signals. Signals are divided into:
deterministic;
random.
Deterministic signals are signals that are precisely determined at any time. In contrast, some parameters of random signals cannot be predicted in advance.
Strictly speaking, since the issuance of a particular message by a message source (for example, a sensor) is random, it is impossible to accurately predict the change in the values of the signal parameters. Consequently, the signal is fundamentally random. Deterministic signals have a very limited independent meaning only for the purpose of setting up and adjusting information and computing technology playing the role of standards.
Depending on the structure of the parameters, signals are subdivided into:
discrete;
continuous;
discrete continuous.
A signal is considered discrete for a given parameter if the number of values that this parameter can take is finite (countable). Otherwise, the signal is considered continuous for this parameter. A signal that is discrete in one parameter and continuous in another is called discrete-continuous.
In accordance with this, the following types of signals are distinguished (Fig. 1.4.):
a) Continuous in level and time (analog) are signals at the output of microphones, temperature sensors, pressure sensors, etc.
b) Continuous in level, but discrete in time. Such signals are obtained by sampling analog signals in time.
Rice. 1.4. Varieties of signals.
By sampling we mean the transformation of a continuous time function (in particular a continuous signal) into a discrete time function representing a sequence of quantities called coordinates, samples or samples (sample value).
The most widespread method is discretization, in which the role of coordinates is played by instantaneous values of a continuous function (signal) taken at certain points in time S (t i), where i = 1,…, n. The time intervals between these moments are called sample intervals. This type of sampling is often referred to as pulse amplitude modulation (PAM).
c) Discrete in level, continuous in time. Such signals are obtained from continuous ones as a result of level quantization.
By level quantization (or simply quantization) is meant the transformation of some quantity with a continuous scale of values (for example, the amplitude of a signal) into a quantity with a discrete scale of values.
This continuous scale of values is divided into 2m + 1 intervals, called quantization steps. Of the set of instantaneous values belonging to the j-th quantization step, only one value S j is allowed, it is called the j-th quantization levels. Quantization is reduced to replacing any instantaneous value of a continuous signal with one of a finite set of quantization levels (usually the closest one):
S j, where j = -m, -m + 1, ..., -1,0,1, ..., m.
The set of S j values forms a discrete scale of quantization levels. If this scale is uniform, i.e. the difference ΔS j = S j - S j-1 is constant, the quantization is called uniform. Otherwise, it will be uneven. Due to the simplicity of technical implementation, uniform quantization has become the most widespread.
d) Discrete in level and time. Such signals are obtained by sampling and quantizing simultaneously. These signals are easy to represent in digital form (digital sample), i.e. in the form of numbers with a finite number of digits, replacing each pulse with a number denoting the number of the quantization level that the pulse reached at a particular time. For this reason, these signals are often referred to as digital signals.
The impetus for the presentation of continuous signals in discrete (digital) form was the need to classify speech signals during World War II. An even greater incentive to digital conversion of continuous signals was the creation of computers, which are used as a source or receiver of signals in many information transmission systems.
Here are some examples of digital conversion of continuous signals. For example, in digital telephone systems (standard G.711), the replacement of an analog signal with a sequence of samples occurs with a frequency of 2F = 8000 Hz, T d = 125 μs. (Since the frequency range of the telephone signal is 300-3400 Hz, and the sampling frequency according to the Nyquist theorem -Kotelnikova should be at least twice the maximum frequency of the converted signal F). Further, each pulse is replaced in an 8-bit analog-to-digital converter (ADC - ADC-Analog-to-Digital Converter) with a binary code that takes into account the sign and amplitude of the sample (256 quantization levels). This quantization process is called Pulse Code Modulation (PCM or PCM). In this case, a non-linear quantization law called "A = 87.6" is used, which better takes into account the nature of human perception of speech signals. The transmission speed of one telephone message turns out to be 8 × 8000 = 64 Kbps. A 30-channel telephone messaging system (the first level of the hierarchy of the CCITT standard - PDH-E1) with time division of channels already operates at a speed of 2048 Kbit / s.
When digital music is recorded on a CD (Compact Disk), containing a maximum of 74 minutes of stereo sound, a sampling frequency of 2F≈44.1 kHz is used (since the hearing limit of the human ear is 20 kHz plus a 10% margin) and 16 bit linear quantization of each sample (65536 levels sound signal, for speech, 7-8 digits are enough).
The use of discrete (digital) signals dramatically reduces the likelihood of obtaining distorted information, because:
in this case, efficient coding techniques are applicable that provide error detection and correction (see Topic 6);
it is possible to avoid the effect of accumulation of distortions inherent in a continuous signal during their transmission and processing, since the quantized signal can be easily restored to its original level whenever the amount of accumulated distortion approaches half the quantization step.
In addition, in this case, the processing and storage of information can be carried out by means of computer technology.
1. Basic concepts and definitions. Definition of radio electronics. Definition of radio engineering. Signal concept. Classification analysis of signals. Classification analysis of radio engineering circuits. Classification analysis of radio electronic systems.
Modern radio electronics is a generalized name for a number of fields of science and technology related to the transmission and transformation of information based on the use and transformation of electromagnetic waves and radio frequency waves; the main areas are:
radio engineering, radio physics and electronics.
The main task of radio engineering is to transmit information over a distance using electromagnetic waves. In a broader sense, modern radio engineering is a field of science and technology associated with the generation, amplification, conversion, processing, storage, transmission and reception of electromagnetic waves in the radio frequency range used to transmit information over a distance. As it follows from this, radio engineering and radio electronics are closely related and often these terms replace each other.
The science that studies the physical foundations of radio engineering is called radiophysics.
1. The concept of a signal.
A signal (from Latin signum - a sign) is a physical process or phenomenon that carries a message about an event, the state of an object, or sends control commands, notifications, etc. Thus, the signal is the material carrier of the message. Any physical process (light, electric field, sound vibrations, etc.) can serve as such a carrier. In electronics, electrical signals are mainly studied and used. Signals as physical processes are observed using various instruments and devices (oscilloscope, voltmeters, receivers). Any model reflects a limited number of the most essential features of a real physical signal. Inessential signal features are ignored to simplify the mathematical description of signals. The general requirement for a mathematical model is the maximum approximation to the real process with the minimum complexity of the model. Functions that describe signals can take real and complex values, so they often talk about real and complex signal models.
Signal classification. According to the predictions of the instant. signal values at any time are separated by:
Deterministic signals, i.e. such signals for which instantaneous values for any moment of time are known and predictable with a probability equal to one;
Random signals, i.e. such signals, the value of which at any moment of time cannot be predicted with a probability equal to one.
All signals carrying information are random, since a completely deterministic signal (known) does not contain information.
The simplest examples of deterministic and random signals are line voltages and noise voltages, respectively (see Figure 2.1).
In turn, random and deterministic signals can be subdivided into continuous or analog signals and discrete signals, which have several varieties. If a signal can be measured (observed) at any time, then it is called analog. Such a signal exists at any time. Discrete signals can be observed and measured in discrete (separate) time intervals limited by the time of occurrence. Discrete signals include pulse signals.
The figure shows two types of pulses. Video impulse and radio impulse. When forming radio pulses, a video pulse is used as a control (modulating) signal, and in this case there is an analytical connection between them: 
In this case, it is called the envelope of the radio pulse, and the function is its filling.
Pulses are usually characterized by amplitude A, duration, duration of the rise and fall and, if necessary, the frequency or repetition period.
Impulse signals can be of various types. In particular, a distinction is made between impulse signals called discrete (see Fig. 2.3).
This kind of signals can be represented by a mathematical model in the form of a countable set of function values - where i = 1, 2, 3, ...., k, counted at discrete times. The sampling step of the signal in time and in amplitude is usually a constant value for a given type of signal, i.e. minimum signal gain
Each of the values of the finite set S can be represented in binary system calculus in the form of a number: - 10101; - 11001; - 10111. Such signals are called digital.
Classification of radio systems and the tasks they solve
According to the functions performed, information radio systems can be divided into the following classes:
information transmission (radio communication, radio broadcasting, television);
extraction of information (radar, radio navigation, radio astronomy, radio measurements, etc.);
destruction of information (radio countermeasures);
control of various processes and objects (unmanned aerial vehicles, etc.);
combined.
In the information transmission system, there is a source of information and its recipient. In a radio system for retrieving information, information as such is not transmitted, but is extracted either from its own signals emitted in the direction of the object under study and reflected from it, or from signals from other radio systems, or from the own radio emission of various objects.
Information destruction radio systems serve to interfere with the normal operation of a competing radio system by emitting an interfering signal, or receiving, deliberately distorting and re-emitting a signal.
In radio control systems, the problem is solved by the object of a command sent from the control panel. Command signals are information for the tracker executing the command.
The main tasks solved by the radio system when receiving information are:
Signal detection in the background of interference.
Distinguishing signals against the background of interference.
Estimation of signal parameters.
Play message.
The first problem is solved most simply, in which, with the given probabilities of correct detection and false alarm, a decision should be made about the presence of a known signal in the received message. The higher the level of the task, the more complex the receiver circuit becomes.
2. Energy, power, orthogonality and coherence of signals. Mutual energy of signals (similarity integral). Signal rate concept.
The purpose of electronic devices, as you know, is to receive, transform, transmit and store information in the form of electrical signals. Signals acting in electronic devices, and accordingly the devices themselves are divided into two large groups: analog and digital.
Analog signal- a signal that is continuous in level and in time, that is, such a signal exists at any time and can take any level from the specified range.
Quantized signal- a signal that can only take certain quantized values corresponding to the quantization levels. The distance between two adjacent levels is the quantization step.
Sampled signal- a signal, the values of which are set only at times, called sampling times. The distance between adjacent sampling points is the sampling step. At constant, Kotelnikov's theorem is applicable:, where is the upper cutoff frequency of the signal spectrum.
Digital signal- signal quantized in level and sampled in time. The quantized values of a digital signal are usually encoded with a certain code, while each sample selected during the sampling process is replaced by a corresponding codeword, the symbols of which have two values - 0 and 1 (Fig. 2.1).
Typical representatives of analog electronics devices are communication devices, radio broadcasting, television. General requirements for analog devices are minimal distortion. The desire to meet these requirements leads to the complication electrical circuits and device designs. Another problem of analog electronics is the achievement of the necessary noise immunity, because in an analog communication channel, noise is fundamentally unavoidable.
Digital signals are generated electronic circuits, transistors in which are either closed (the current is close to zero), or completely open (the voltage is close to zero), so they dissipate insignificant power and reliability digital devices turns out to be higher than analog.
Digital devices are more immune to interference than analog ones, since small extraneous disturbances do not cause erroneous operation of devices. Errors appear only in the case of such disturbances in which a low signal level is perceived as high, or vice versa. In digital devices, you can also apply special codes to correct errors. There is no such possibility in analog devices.
Digital devices are insensitive to the spread (within acceptable limits) of the parameters and characteristics of transistors and other circuit elements. Digital devices that are error-free do not need to be tuned, and their characteristics are completely repeatable. All this is very important in the mass production of devices using integrated technology. The cost-effectiveness of the production and operation of digital integrated circuits has led to the fact that in modern radio electronic devices, not only digital, but also analog signals are digitally processed. Digital filters, regulators, multipliers, etc. are widespread. Before digital processing, analog signals are converted into digital using analog-to-digital converters (ADC). Reverse conversion - restoration of analog signals to digital - is performed using digital-to-analog converters (DAC).
With all the variety of tasks solved by digital electronics devices, their functioning occurs in number systems operating with only two digits: zero (0) and one (1).
The operation of digital devices is usually clocked a sufficiently high frequency clock generator. During one clock cycle, the simplest micro-operation is realized - reading, shift, logical command, etc. Information is presented in the form of a digital word. To transfer words, two methods are used - parallel and sequential. Serial coding is used in the exchange of information between digital devices (for example, in computer networks, modem communications). Information processing in digital devices is implemented using parallel information coding, which ensures maximum performance.
The element base for building digital devices is integrated circuits(IC), each of which is implemented using a certain number of logical elements - the simplest digital devices that perform elementary logical operations.
A signal is defined as a voltage or current that can be transmitted as a message or information. All signals are analog by nature, be they AC or DC, digital or pulsed. However, it is common to distinguish between analog and digital signals.
A digital signal is a signal that has been processed in a certain way and converted into numbers. Usually these digital signals are associated with real analog signals, but sometimes there is no connection between them. An example is the transfer of data in local computer networks(LAN) or other high-speed networks.
In digital signal processing (DSP), an analog signal is converted to binary form by a device called an analog-to-digital converter (ADC). The ADC outputs a binary representation of the analog signal, which is then processed by an arithmetic digital signal processor (DSP). After processing, the information contained in the signal can be converted back to analog form using a digital-to-analog converter (DAC).
Another key concept in signal definition is the fact that a signal always carries some information. This leads us to the key problem of physical analog signal processing - the problem of information retrieval.
Signal processing objectives.
The main purpose of signal processing is the need to obtain the information they contain. This information is usually present in the amplitude of a signal (absolute or relative), in frequency or in spectral composition, in phase or in the relative time dependences of several signals.
Once the desired information has been extracted from the signal, it can be used in a variety of ways. In some cases, it is desirable to reformat the information contained in the signal.
In particular, the signal format change occurs when the audio signal is transmitted in a frequency division multiple access (FDMA) telephone system. In this case, analog techniques are used to place multiple voice channels in the frequency spectrum for transmission via microwave radio relay, coaxial or fiber optic cable.
When digital communication analog audio information is first converted to digital using an ADC. Digital information representing individual audio channels is time multiplexed (time division multiplexing, TDMA) and transmitted over a serial digital link (as in a PCM system).
Another reason for signal processing is to compress the signal bandwidth (without significant loss of information), followed by formatting and transmission of information at lower rates, which allows you to narrow the required channel bandwidth. High speed modems and adaptive pulse code modulation (ADPCM) systems widely use data redundancy (compression) algorithms, as do digital mobile communication systems, MPEG audio recording systems, and high definition television (HDTV).
Industrial data acquisition and control systems use information from sensors to generate appropriate signals feedback, which, in turn, directly control the process. Note that these systems require both ADCs and DACs as well as sensors, signal conditioners, and DSPs (or microcontrollers).
In some cases, there is noise in the signal containing the information, and the main goal is to recover the signal. Techniques such as filtering, autocorrelation, convolution, etc. are often used to accomplish this task in both the analog and digital domains.
PURPOSES OF SIGNAL PROCESSING- Extraction of signal information (amplitude, phase, frequency, spectral components, temporal relationships)
- Signal format conversion (telephony with channel division FDMA, TDMA, CDMA)
- Data compression (modems, Cell Phones, HDTV television, MPEG compression)
- Formation of feedback signals (industrial process control)
- Separation of signal from noise (filtering, autocorrelation, convolution)
- Isolation and storage of a signal in digital form for further processing (FFT)
Signal shaping
In most of these situations (related to the use of DSP technologies), both an ADC and a DAC are needed. However, in some cases only a DAC is required where analog signals can be directly generated from the DSP and DAC. A good example are video scanned displays in which a digitally generated signal drives the video image or a RAMDAC unit (pixel array converter from digital to analog).
Another example is artificially synthesized music and speech. In fact, the generation of physical analog signals using only digital techniques relies on information previously obtained from sources of such physical analog signals. In display systems, the data on the display must convey relevant information to the operator. When developing sound systems are set by the statistical properties of the generated sounds, which have been pre-determined using the widespread use of DSP methods (sound source, microphone, preamplifier, ADC, etc.).
Signal processing methods and technologies
Signals can be processed using analog techniques (analog signal processing, or ASP), digital techniques (digital signal processing, or DSP), or a combination of analog and digital techniques (combined signal processing, or MSP). In some cases the choice of methods is clear, in other cases there is no clarity in the choice and the final decision is based on certain considerations.
As for DSP, its main difference from traditional computer data analysis is high speed and the efficiency of performing complex digital processing functions such as filtering, leveraged analysis, and data compression in real time.
Combined signal processing means that the system performs both analog and digital processing. Such a system can be implemented as a printed circuit board, a hybrid integrated circuit (IC), or a single chip with integrated elements. ADCs and DACs are considered as combined signal processing devices, since each of them implements both analog and digital functions.
Recent advances in VLSI technology enable complex (digital and analog) processing on a single chip. The very nature of DSP implies that these functions can be performed in real time.
Comparison of analog and digital signal processing
Today's engineer is faced with choosing the right combination of analog and digital methods to solve a signal processing problem. It is impossible to process physical analog signals using only digital methods, since all sensors (microphones, thermocouples, piezoelectric crystals, drive heads on magnetic disks etc.) are analog devices.
Some types of signals require normalization circuits for further signal processing, both analog and digital. Signal normalization circuits are analog processors that perform functions such as amplification, accumulation (in measuring and preliminary (buffer) amplifiers), signal detection against a background of noise (high-precision common-mode amplifiers, equalizers and linear receivers), dynamic range compression (logarithmic amplifiers, logarithmic DACs and programmable gain amplifiers) and filtering (passive or active).
Several methods for implementing the signal processing are shown in Figure 1. The top area of the figure shows a purely analog approach. The rest of the areas show the DSP implementation. Note that once DSP technology is selected, the next solution should be to locate the ADC in the signal processing path.
ANALOGUE AND DIGITAL SIGNAL PROCESSING
Figure 1. Signal processing methods
In general, since the ADC has been moved closer to the sensor, most of the analog signal processing is now done by the ADC. The increase in ADC capabilities can be expressed in increasing the sampling rate, expanding the dynamic range, increasing the resolution, cutting off input noise, using input filtering and programmable amplifiers (PGA), the presence of on-chip voltage references, etc. All mentioned additions increase the functional level and simplify the system.
In the presence of modern technologies high sampling rates and high resolution DACs and ADCs, significant progress has been made in integrating an increasing number of circuits directly into the ADC / DAC.
In the measurement field, for example, there are 24-bit ADCs with built-in programmable amplifiers (PGAs) that allow full-scale 10 mV bridge signals to be digitized directly without further normalization (eg AD773x series).
At voice and audio frequencies, complex encoder-decoding devices - codecs (Analog Front End, AFE) - are common, which have an analog circuit built into the microcircuit that meets the minimum requirements for external normalization components (AD1819B and AD73322).
There are also video codecs (AFE) for tasks such as CCD image processing and others (such as the AD9814, AD9816, and AD984X series).
Implementation example
As an example of using a DSP, compare analog and digital low pass filters (LPFs), each with a cutoff frequency of 1 kHz.
The digital filter is implemented as a typical digital system shown in Figure 2. Notice that there are several implicit assumptions in the diagram. First, in order to accurately process the signal, it is assumed that the ADC / DAC path has sufficient sampling rate, resolution and dynamic range. Second, in order to complete all of its computations within the sampling interval (1 / f s), the DSP device must be fast enough. Thirdly, at the ADC input and DAC output there is still a need for analog filters for limiting and restoring the signal spectrum (anti-aliasing filter and anti-imaging filter), although the requirements for their performance are not high. With these assumptions in place, you can compare digital and analog filters.
Figure 2. Structural scheme digital filter
The required cutoff frequency for both filters is 1 kHz. Analog conversion is of the first kind of the sixth order (characterized by the presence of ripple in the transmission ratio in the passband and the absence of ripple outside the passband). Its characteristics are shown in Figure 2. In practice, this filter can be represented by three second-order filters, each of which is built on an operational amplifier and several capacitors. By using modern systems Computer-aided design (CAD) filters It is easy to create a sixth-order filter, but accurate component selection is required to meet the 0.5 dB flatness specification.
The 129-factor digital FIR filter shown in Figure 2 has a flatness of only 0.002 dB in passband, a linear phase response, and a much steeper roll-off. In practice, such characteristics cannot be realized using analog methods. Another obvious advantage of the circuit is that the digital filter does not require selection of components and is not subject to parameter drift, since the filter's clock frequency is stabilized by a crystal resonator. A filter with 129 coefficients requires 129 multiply-and-accumulate (MAC) operations to compute the output sample. These calculations must be completed within the 1 / fs sampling interval in order to operate in real time. In this example, the sampling rate is 10 kHz, so 100 µs is sufficient for processing if there is no significant additional computation required. The ADSP-21xx DSP family can complete the entire multiply-accumulate process (and other functions required to implement the filter) in one instruction cycle. Therefore, a 129-factor filter requires over 129/100 μs = 1.3 million operations per second (MIPS). Existing DSPs are much faster and are therefore not a limiting factor for these applications. The 16-bit fixed-point ADSP-218x series achieves up to 75MIPS performance. Listing 1 shows the assembly code that implements the filter on the ADSP-21xx DSP processors. Note that the actual lines of the executable code are marked with arrows; the rest is comments.
Figure 3.Analog and digital filters
Of course, in practice, there are many other factors considered when comparing analog versus digital filters, or analog versus digital signal processing techniques in general. Modern signal processing systems combine analog and digital methods to achieve the desired function and take advantage of the best methods, both analog and digital.
ASSEMBLY PROGRAM:
FIR FILTER FOR ADSP-21XX (SINGLE PRECISION)
MODULE fir_sub; (FIR filter subroutine Call parameters of subroutine I0 -> Oldest data in delay line I4 -> Start of filter coefficient table L0 = Filter length (N) L4 = Filter length (N) M1, M5 = 1 CNTR = Filter length - 1 (N-1) Returned values MR1 = Summation result (rounded and limited) I0 -> Oldest data in delay line I4 -> Start of filter coefficient table Variable registers MX0, MY0, MR Runtime (N - 1) + 6 cycles = N + 5 cycles All odds are written in 1.15 format) .ENTRY fir; fir: MR = 0, MX0 = DM (I0, M1), MY0 = PM (I4, M5) CNTR = N-1; DO convolution UNTIL CE; convolution: MR = MR + MX0 * MY0 (SS), MX0 = DM (I0, M1), MY0 = PM (I4, M5); MR = MR + MX0 * MY0 (RND); IF MV SAT MR; RTS; .ENDMOD; REAL TIME SIGNAL PROCESSING
Literature:
Together with the article "Types of signals" read:
Which must be accepted by the receiving party, otherwise it is not a message. The signal can be any physical process, the parameters of which change in accordance with the transmitted message.
A signal, deterministic or random, is described by a mathematical model, a function that characterizes the change in signal parameters. The mathematical model for representing a signal as a function of time is the fundamental concept of theoretical radio engineering, which turned out to be fruitful both for the analysis and for the synthesis of radio engineering devices and systems. In radio engineering, an alternative to a signal that carries useful information is noise - usually a random function of time that interacts (for example, by adding) with the signal and distorts it. The main task of theoretical radio engineering is to extract useful information from the signal with the obligatory consideration of noise.
Concept signal allows one to abstract from a specific physical quantity, for example, current, voltage, acoustic wave, and to consider outside the physical context the phenomena associated with encoding information and extracting it from signals that are usually distorted by noise. In research, a signal is often represented as a function of time, the parameters of which can carry the necessary information. The recording method of this function, as well as the recording method of interfering noise, is called mathematical signal model.
In connection with the concept of a signal, the following are formulated basic principles cybernetics, as the concept of the bandwidth of a communication channel, developed by Claude Shannon and the optimal reception, developed by V.A.Kotelnikov.
Signal classification
By the physical nature of the information carrier:
- electrical;
- electromagnetic;
- optical;
- acoustic
By the method of setting the signal:
- regular (deterministic) given by an analytical function;
- irregular (random), taking arbitrary values at any time. The apparatus of the theory of probability is used to describe such signals.
Depending on the function describing the signal parameters, analog, discrete, quantized and digital signals are distinguished:
- continuous (analog) described by a continuous function;
- discrete, described by a function of samples taken at certain points in time;
- level quantized;
- discrete signals quantized by level (digital).
Analog signal (AC)
Analog signal
Most of the signals are analog in nature, that is, they change continuously in time and can take on any values over a certain interval. Analog signals are described by some mathematical function of time.
An example of an AC is a harmonic signal - s (t) = A cos (ω t + φ).
Analog signals are used in telephony, radio broadcasting, television. It is impossible to enter such a signal into a computer and process it, since at any time interval it has an infinite set of values, and for an accurate (without error) representation of its value, numbers of infinite bit width are required. Therefore, it is necessary to convert the analog signal so that it can be represented by a sequence of numbers of a given bit width.
Discrete signal
Sampling of an analog signal means that the signal is represented as a sequence of values taken at discrete moments in time. These values are called counts.Δt is called sampling interval.
Quantized signal
Main article: Quantization (computer science)
During quantization, the entire range of signal values is divided into levels, the number of which must be represented in numbers of a given bit width. The distance between these levels is called the quantization step Δ. The number of these levels is N (from 0 to N-1). A certain number is assigned to each level. The signal samples are compared with the quantization levels, and a number corresponding to a certain quantization level is selected as a signal. Each quantization level is coded as a binary number with n bits. The number of quantization levels N and the number of bits n of binary numbers encoding these levels are related by the relationship n ≥ log 2 (N).
Digital signal
In order to represent an analog signal as a sequence of numbers of finite length, it must first be converted into a discrete signal and then quantized. Quantization is a special case of sampling, when sampling occurs in the same quantity called a quantum. As a result, the signal will be represented in such a way that an approximate (quantized) value of the signal is known at each given time interval, which can be written as an integer. If you write these integers in the binary system, you get a sequence of zeros and ones, which will be a digital signal.
Signal and event
An event (receipt of a note, observation of a signal flare, reception of a symbol by telegraph) is a signal only in that system of relations in which the message is recognized as significant (for example, in combat conditions, a signal flare is an event that is significant only for the observer to whom it is addressed). Obviously, a signal given analytically is not an event and does not carry information if the signal function and its parameters are known to the observer.
In technology, a signal is always an event. In other words, an event - a change in the state of any component of a technical system, recognized by the logic of the system as significant, is a signal. An event that is not recognized by this system of logical or technical relations as significant is not a signal.
Signal presentation and spectrum
There are two ways to represent a signal, depending on the domain of definition: time and frequency. In the first case, the signal is represented as a function of time characterizing the change in its parameter.
In addition to the usual temporal representation of signals and functions, the description of signals by functions of frequency is widely used in the analysis and processing of data. Indeed, any signal, arbitrarily complex in its form, can be represented as a sum of more than simple signals, and, in particular, in the form of the sum of the simplest harmonic vibrations, the collection of which is called frequency spectrum signal.
To switch to the frequency representation, the Fourier transform is used:
.
The function is called the spectral function or spectral density.
Since the spectral function is complex, we can talk about the spectrum of amplitudes and the spectrum of phases. The physical meaning of the spectral function: the signal is represented as the sum of an infinite series of harmonic components (sinusoids) with amplitudes continuously filling the frequency range from 0 to, and initial phases.
Wikimedia Foundation. 2010.
Synonyms:See what "Signal" is in other dictionaries:
signal- a, m. signal, it. Signal cf. lat. signale lat. signum sign, signal. 1. Conventional sign for the transfer of what l. information, orders, etc. UAS 1. When on the ship the commander's chief is so damaged in battle that he can no longer serve, then ... ... Historical Dictionary of Russian Gallicisms
Cm … Synonym dictionary
In physics, a change in some physical quantity that serves to register an event. See also: Signals of the Reference System Finam Financial Dictionary. Signal Signal is the process of communicating information through the actions of a company. In English: Signal Synonyms:…… Financial vocabulary
