What is an electrical signal and what is it used for? Let's discuss in this article.
A signal is something that can be transmitted through space and time. So, what conditions must exist to call a signal a “signal”?
Firstly, with The signal must be created (generated) by someone.
Secondly, the signal must be intended for whom.
Thirdly, someone must accept this signal and draw some conclusions for themselves, that is, interpret the signal correctly.
Let's plunge into the Wild West.
I think it's no secret that the Indians lit a fire, and the smoke from the fire was used to transmit a signal. This means that in our case the fire is a signal generator. So, the first point works).Who was the smoke from the fire intended for? For cowboys? Of course not! For our own Indians. So point two works. Okay, you saw two columns of smoke rising into the sky. Does this mean anything to you? Someone is probably grilling kebabs? May be. But if you approach these fires, then they will make a shashlik out of you). For the Indians, these two columns of smoke meant that their detachment had successfully hunted cowboys ;-). Well, the third rule has been fulfilled ;-).
But what is an electrical signal? I am tormented by vague doubts that somewhere there is an electric current involved :-). How is electric current characterized? Well, of course, voltage and current. The most remarkable thing is that electric current is very convenient to transmit through space using wires. In this case, its speed of propagation will be equal to the speed of light. Although the electrons in the conductor move at a speed of only a few millimeters per second, the electric field immediately covers the entire wire at the speed of light! And as you remember, the speed of light is 300,000 kilometers per second! Therefore, the electron at the other end of the wire will almost immediately begin to move.
Transmission of electrical signals
So, we will use wires to transmit a signal through space. A little higher we examined the conditions for the occurrence of a signal. So, first of all, we need a generator of these signals! That is, it could be some kind of battery or circuit that would generate electric current. Next, there must be someone who would receive this signal. This could be some kind of load, such as a light bulb, a heating element, or an entire circuit that would receive this signal. And thirdly, the load must somehow react to this signal. The light bulb should emit light heating element– to warm up, and the circuit to perform some function.
As you understand from all of the above, the main trump card of a signal is its generator. So, as we have already discussed, two parameters can be transmitted over the wires electric current –this is voltage and current. That is, we can create a generator that would change either its voltage or current in the load, which would cling through the wires to this generator. Basically, in electronics, it is the “voltage” parameter that is used, since the voltage is easy to obtain and change its value.
Time and electrical signal
As I said, the signal is transmitted in time and space. That is, time is an important parameter for an electrical signal. Now we will have to sweat a little and remember the mathematics and physics course for high school. Let's remember the Cartesian coordinate system. As you remember, we plotted the Y axis vertically and the X axis horizontally:
In electronics and electrical engineering, we plot time along X, let's call it t, and vertically we plot voltage, call it U. As a result, our coordinate system will look like this:
A device that shows us the change in voltage over time is called oscilloscope, and the graph of this voltage is called oscillogram. An oscilloscope can be:
or analog:
Types of electrical signals
D.C
What electrical signal is the simplest signal in electronics? I think it's DC signal. What does direct current mean? This is a current whose voltage value does not change over time. How does it look on our graph? Something like this:
Here we see a 3 volt DC signal.
Vertically we have voltage in volts, and horizontally – well, let’s say, in seconds. Direct current always has the same voltage value over time, so it doesn’t matter whether we count in seconds or in hours. The tension neither jumped nor fell. It was 3 Volts and remains so. That is, we can say that the direct current signal is a straight line parallel to the time axis t.
This is what a DC signal looks like on an analog oscilloscope
What kind of electric current generators can produce such a constant voltage signal?
These are, of course, different batteries
mobile phone batteries
for laptop
car batteries
and other chemical current sources.
In laboratory conditions, it is easier to obtain a constant voltage from an alternating voltage. A device that can do this is called a laboratory constant voltage power supply.
Noise signal or just noise
What will happen if the tension becomes chaotic? You'll get something like this:
This electrical signal is called noise.
I think this is the first time some of you are seeing a noise waveform, but I am 100% sure that everyone heard the sound of this signal ;-). Well, click on Play ;-)
The hiss of a radio receiver or an old TV that is not tuned to a station or any channel is noise ;-) No matter how strange it may sound, such a signal is also very often used in electronics. For example, you can assemble a frequency jammer circuit that would extinguish all television and radio receivers within a kilometer radius). That is, we generate a noise signal, amplify it and send it on the air ;-) As a result, we jam all the transceiver equipment.
Sine wave
The sine wave is the most favorite signal among electronics engineers.
Everyone loves to swing on a swing?
Here we see a girl happily swinging on them. But suppose she doesn’t know the trick that you can swing yourself by bending and straightening your legs in time. Therefore, the girl’s father came and pushed his daughter forward.
The graph below shows exactly this case.
As you can see, the girl's trajectory through time turned out to be very funny. This movement schedule is called “ sine wave“. In electronics, such a signal is called sinusoidal. It seems like a painfully simple graph, but you won’t believe it, it’s this simple sine wave that all electronics are built on.
Because sine wave repeats its shape throughout the entire time, then it can be called periodic. That is, you eat lunch periodically - in periods - equal periods of time. It's the same here. This signal periodically repeats itself. Important parameters of periodic signals are amplitude, period and frequency.
Amplitude (A) – maximum voltage deviation from zero to a certain value.
Period (T) – time during which the signal is repeated again. That is, if you have lunch today at 12:00, tomorrow also at the same time, at 12:00, and the day after tomorrow also at the same time, then your lunch takes place over a period of 24 hours. Everything is elementary and simple ;-)
Frequency (F) – it’s just one divided by a period, that is
Measured in Hertz. Explained as “so many vibrations per second.” Well, that's enough to start with for now ;-).
As I already said, the sine wave plays a very important role in electronics. You don't even have to go far. It is enough to stick the oscilloscope probes into your home outlet, and you can already observe a sinusoidal signal with a frequency of 50 Hertz and an amplitude of 310 Volts.
Square wave
Very often in electronics a rectangular signal is used:
The square wave in the figure below, where the pause time and the duration time of the signal are equal, is called meander.
Triangle signal
Close friends of the sine wave are triangle signal
The triangle signal has a very close sidekick - this sawtooth signal
Complex signal
Also used in electronics complex signals . Here, for example, is one of them (I drew it out of the blue):
All these signals refer to periodic signals, since for them you can specify period, frequency following and amplitude the signals themselves:
Bipolar signals
For signals that “pierce the floor”, that is, they can have a negative voltage value, such as these signals
In addition to period and amplitude, they have one more parameter. It's called scope or double amplitude. In bourgeois language it sounds like amplitude Peak-to-peak, which literally translates as “amplitude from peak to peak.”
Here is the double amplitude for a sine wave (2A)
but for a triangular signal:
Most often it is designated as 2A, which tells us that this is a double amplitude signal.
Pulse signals
There are also signals that do not obey the periodic law, but also play an important role in electronics.
Impulses- these are the same signals, but they do not obey the periodic law, and change their meaning depending on the situation.
For example, here is a series of impulses:
Each pulse has a different duration in time, so we cannot talk about any periodicity of the signals.
Beep
There is also a sound signal
Even though he looks like white noise, but carries information in the form of sound. If such an electrical signal is applied to the dynamic head, then you can hear some kind of recording.
Conclusion
Currently, electrical signals play a very important role in radio electronics. Without them, no electronics would exist, let alone digital ones. Currently, digital electronics has reached its apogee, thanks to digital signals and complex system encoding. The data transfer speed is simply stunning! This can be gigabytes of information per second. But it all once began with a simple telegraph...
Analog signal is a continuous function of a continuous argument, i.e. defined for any value of the independent variable. Sources of analog signals, as a rule, are physical processes and phenomena that are continuous in their development (the dynamics of changes in the values of certain properties) in time, in space or in any other independent variable, while the recorded signal is similar (analogous) to the process generating it. An example of a mathematical notation for a specific analog signal: y(t) = 4.8exp[-( t-4) 2 /2.8]. An example of a graphical display of this signal is shown in Fig. 2.2.1, while both the numerical values of the function itself and its arguments can take on any values within certain intervals y£1 y £ y 2,t£1 t £ t 2. If the intervals of signal values or its independent variables are not limited, then by default they are assumed to be equal to -¥ to +¥. Many possible values signal forms a continuous space in which any point can be determined with infinite accuracy.
Rice. 2.2.1. Graphical display of the signal y(t) = 4.8 exp[-( t-4) 2 /2.8].
Discrete signal in its values it is also a continuous function, but defined only by discrete values of the argument. According to the set of its values, it is finite (countable) and is described by a discrete sequence y(n×D t), Where y£1 y £ y 2, D t- interval between samples (signal sampling interval), n = 0, 1, 2, ..., N– numbering of discrete reading values. If a discrete signal is obtained by sampling an analog signal, then it represents a sequence of samples, the values of which are exactly equal to the values of the original signal in coordinates n D t.
An example of sampling an analog signal shown in Fig. 2.2.1, is shown in Fig. 2.2.2. At D t= const (uniform data sampling) a discrete signal can be described by the abbreviated notation y(n).
When the signal is unevenly sampled, the designations of discrete sequences (in text descriptions) are usually enclosed in curly brackets - ( s(t i)), and the reading values are given in the form of tables indicating the coordinate values t i. For short, uneven number sequences, the following numerical description is also used: s(t i) = {a 1 , a 2 , ..., a N}, t = t 1 , t 2 , ..., t N.
Digital signal quantized in its values and discrete in its argument. It is described by a quantized lattice function y n = Q k[y(n D t)], Where Q k- quantization function with the number of quantization levels k, while quantization intervals can be either uniform or uneven, for example, logarithmic. A digital signal is specified, usually in the form of a numeric array of successive values of the argument at D t = const, but, in the general case, the signal can also be specified in the form of a table for arbitrary argument values.
Essentially, a digital signal is a formalized version of a discrete signal when the values of the latter are rounded to a certain number of digits, as shown in Fig. 2.2.3. IN digital systems and in a computer, the signal is always represented accurate to a certain number of bits and therefore is always digital. Taking these factors into account, when describing digital signals, the quantization function is usually omitted (implied uniform by default), and the rules for describing discrete signals are used to describe signals.
Rice. 2.2.2. Discrete signal Fig. 2.2.3. Digital signal
y(n D t) = 4.8 exp[-( n D t-4) 2 /2.8], D t= 1. y n = Q k, D t=1, k = 5.
In principle, an analog signal recorded by appropriate digital equipment can also be quantized in its values (Fig. 2.2.4). But it makes no sense to separate these signals into a separate type - they remain analog piecewise continuous signals with a quantization step, which is determined by the permissible measurement error.
Most of the discrete and digital signals you deal with are sampled analog signals. But there are signals that initially belong to the discrete class, for example gamma rays.
Rice. 2.2.4. Quantized signal y(t)= Qk, k = 5.
Spectral representation of signals. In addition to the usual time (coordinate) representation of signals and functions, when analyzing and processing data, the description of signals by frequency functions is widely used, i.e. by arguments inverse to the arguments of the time (coordinate) representation. The possibility of such a description is determined by the fact that any signal, no matter how complex in its shape, can be represented as a sum of simpler signals, and, in particular, as a sum of the simplest harmonic oscillations, the totality of which is called the frequency spectrum of the signal. Mathematically, the signal spectrum is described by functions of the amplitude values and initial phases of harmonic oscillations using a continuous or discrete argument - frequency. The amplitude spectrum is usually called amplitude-frequency response(frequency response) of the signal, spectrum of phase angles – phase-frequency response(FCHH). Description frequency spectrum displays the signal as unambiguously as the coordinate description.
In Fig. Figure 2.2.5 shows a segment of the signal function, which is obtained by summing the constant component (the frequency of the constant component is 0) and three harmonic oscillations. Mathematical description signal is determined by the formula:
Where A n= (5, 3, 6, 8) - amplitude; fn= (0, 40, 80, 120) - frequency (Hz); φ n= (0, -0.4, -0.6, -0.8) - initial phase angle (in radians) of oscillations; n = 0,1,2,3.
Rice. 2.2.5. Temporal representation of the signal.
The frequency representation of this signal (signal spectrum in the form of frequency response and phase response) is shown in Fig. 2.2.6. Please note that the frequency representation of a periodic signal s(t), limited in the number of harmonics of the spectrum, is only eight samples and is very compact compared to the continuous time representation, defined in the interval from -¥ to +¥.
Rice. 2.2.6. Frequency representation of the signal.
Graphic display analog signals (Fig. 2.2.1) do not require any special explanation. When graphically displaying discrete and digital signals, either the method of direct discrete segments of the corresponding scale length above the argument axis is used (Fig. 2.2.6), or the method of an envelope (smooth or broken) based on sample values (dotted curve in Fig. 2.2.2). Due to the continuity of fields and, as a rule, the secondary nature of digital data obtained by sampling and quantization of analog signals, we will consider the second method of graphic display to be the main one.
Types of signals
Signal
Signal is a physical process, some characteristic of which carries informational meaning.
For example, a light signal (light flux) is characterized by brightness, color, polarization properties, direction of propagation, etc.
Information can be carried by either one of these characteristics or a simultaneous combination of several characteristics.
A signal arises in nature during the interaction of material objects and carries information about this interaction. The signal is capable of moving and propagating in some material environment, thereby providing spatial transfer of information from the object (event source) to the subject (observer). The material medium in which the signal propagates is called signal carrier.
Signals differ primarily in their physical nature. Examples: light signal, sound signal, electrical signal, radio signal...
Depending on the source generating them, signals can be natural or artificial.
Natural signals arise due to the fact that material objects interact somewhere in living or inanimate nature. This is a natural process and has nothing to do with human activity. Examples: the glow of the Sun, the singing of birds, the spread of the smell of flowers...
Artificial signals are initiated by humans or arise in technical systems created by man. Examples: telephone line electrical signals; radio signals; flare or fire; traffic light signal; fire truck siren...
The shape of the signals is analog, discrete And digital.
Analog (or continuous) signal is a physical process whose information characteristics change smoothly. For example, a smoothly varying electrical signal (Fig. 1). Other examples: sound signal, natural light signal. Almost all natural signals are analog.
A feature of an analog signal is the blurring of the boundary between its two adjacent values. The total number of values that can characterize an analog signal is infinitely large.
Discrete signal is a physical process, the information characteristic of which changes abruptly and can only take on a certain limited set of values (Fig. 2).
The peculiarity of a discrete signal is a clear distinction between two different signal values. The total number of possible values that a discrete signal can take is always limited.
For example, a lamp included in electrical circuit. The lamp can either be on or off. If the lamp is on, this serves as a signal that there is current in the circuit. If it doesn't light up, there is no current. Intermediate values (how bright the lamp is lit) are not taken into account here - there are only two values: either it is on or it is not on.
Another example: some message is transmitted by telegraph.
The message is transmitted using Morse code, which uses three different values: dot, dash and space (pause). The signal that this message carries will also have only three different meanings: a short signal, a long signal, and no signal. Since the number of possible signal values is limited, it is a discrete signal.
Discrete signals are usually artificial(created by a person or a technical system).
By types (types) of signals the following stand out:
- analog
- digital
- discrete
Analog signal
Analog signal is natural. It can be fixed using various types sensors For example, environmental sensors (pressure, humidity) or mechanical sensors (acceleration, speed). Analog signals in mathematics they are described by continuous functions. Electrical voltage is described using a straight line, i.e. is analog.
Digital signal
Digital the signals are artificial, i.e. they can only be obtained by converting an analog electrical signal.
The process of sequentially converting a continuous analog signal is called sampling. There are two types of discretization:
- by time
- by amplitude
Time sampling is usually called a sampling operation. And sampling by signal amplitude is quantization by level.
Mostly digital signals are light or electrical impulses. A digital signal uses the entire given frequency (bandwidth). This signal still remains analog, only after conversion it is endowed with numerical properties. And you can apply numerical methods and properties to it.
Discrete signal
Discrete signal– this is still the same converted analog signal, only it is not necessarily quantized in level.
This is the basic information about types (types) of signals.
Test
Signal types
Introduction
signal electronic sensor
Electronics is a science that studies the interaction of electrons or other charged particles with electromagnetic fields and the development of methods for creating electronic devices and devices that use this interaction to transmit, store and transmit information.
The results of the study of electronic processes and phenomena, as well as the research and development of methods for creating electronic instruments and devices, determine the development of electronic technology in two directions. The first of them is associated with the creation of production technologies and industrial production of electronic devices for various purposes. The second direction is associated with the creation, based on these devices, of equipment for solving various types of problems related to the transmission, reception and conversion of information in the field of computer science, computer technology, process automation systems, etc.
Electronics has a short but eventful history. Its first period is associated with the simplest transmitters and receivers capable of perceiving their signals. Then came the era of vacuum tubes. Since the mid-50s, a new period in the development of electronics began, associated with the advent of semiconductor elements, and then small and large integrated circuits.
The current stage of electronics development is characterized by the emergence of microprocessor ultra-large-scale integrated circuits, digital signal processors, programmable logic integrated circuits, which allow solving signal processing problems at high technical and economic indicators. Digital electronics, which has transformed systems for collecting, processing and transmitting information, is unthinkable without analog technologies. It is analog devices that largely determine the characteristics of these systems.
Electronics studies issues of transmitting, receiving and converting information based on electromagnetic phenomena. In relation to electronics, along with the transmission of messages from person to person, it is also advisable to consider the exchange of information between a person and a machine and between machines.
There are many definitions of the concept of information, from the most general philosophical (information is a reflection of the real world) to practical (information is all information that is the object of storage, transmission, transformation).
Information is transmitted in the form of signals. A signal is a physical process that carries information. The signal can be sound, light, in the form postal item etc. The most common signal is in electrical form in the form of voltage versus time U(t).
Almost any electronic system has the purpose of its functioning in one way or another to transform energy or transform information. The task of any electronic control system in the most general sense is to process information about the current operating mode of the controlled object and, based on this, generate control signals in order to bring the current operating mode of the object closer to the specified mode. In this case, information processing means solving the system state equations in one way or another.
The object presented in Fig. 1.1 is a real physical object, the numerous properties of which are characterized by various physical quantities (PV). It is in multilateral and complex connections with other objects. Of all the variety of these connections in Fig. Figure 1.1 shows the input PV X and output PV Y to be measured, characterizing the state of the object. Sensors (primary converters) ensure the conversion of PV X and Y, which in most cases are of a non-electrical nature, into electrical signals while maintaining necessary information about disturbing influences and the state of the object.
The signal primary processing device (PDU) is an integral part of the system. It ensures the interface of sensors with subsequent electronic devices that perform preliminary processing of the measured physical quantities. As a rule, it is assigned the following functions:
· output amplification primary converters;
· normalization of analog signals, i.e. bringing the scale boundaries of the primary continuous signal to one of the standard ranges of the input signal of the analog-to-digital converter of the measuring channel (the most common ranges are from 0 to 5 V, from -5 V to 5 V and from 0 to 10 V;
· preliminary low-pass filtering, i.e. limiting the frequency band of the primary continuous signal in order to reduce the influence of interference of various origins on the measurement result;
· ensuring galvanic isolation between the analog or discrete signal source and the measuring and/or status channels of the system. This equally applies to the isolation between the system's discrete output channels and the controlled power equipment. In addition to the actual protection of output and input circuits, galvanic isolation makes it possible to reduce the impact of interference on the system through grounding circuits due to the complete separation of the computer system ground and the controlled equipment ground. The absence of galvanic isolation is allowed only in technically justified cases.
The output signals of the primary processing device are converted into digital form by a device called an analog-to-digital converter (ADC). The ADC output produces a binary representation of the analog signal, which is then processed by a digital signal processor. After processing, the information contained in the signal can be converted back to analog form using a digital-to-analog converter (DAC).
The processor processes initial data characterizing disturbances and the state of the object. The processing algorithm is determined by the object of measurement, the measurement task, which consists in determining the values of selected (measured) physical quantities (PV) with the required accuracy under given conditions, and the main characteristics of measurements.
1. Signals
signal electronic sensor
The concept of signal is one of the basic concepts of electronics. A signal is a physical process existing in a system, which has many states that it assumes in accordance with external influences on this system. The main property of a signal is that it carries information about the impact on this system.
Since real physical processes occur in time, time functions reflecting changes in physical processes are used as a mathematical model of the signal representing these processes.
The signal can be sound, light, in the form of mail, etc. The most common signal is in electrical form in the form of voltage versus time U(t).
. Signal classification
Based on their role in transmitting specific information, signals can be divided into useful and interfering (interference). Useful signals carry specified information, and interference distorts it, although they may also carry other information.
According to the degree of certainty of the expected signal values, all signals can be divided into deterministic signals and random signals. Deterministic is a signal whose value at any time can be accurately determined. Deterministic signals can be periodic or non-periodic.
A signal is called periodic for which the condition is satisfied
s(t) = s (t + kT), where k is any integer, T is a period, which is a finite period of time. An example of a periodic signal is a harmonic oscillation. .
Here U m, T, f 0, w 0, And j 0- amplitude, period, frequency, angular frequency and initial phase of oscillation, respectively.
Complex periodic signals include pulse signals various shapes (electrical impulses)
An electrical impulse is a short-term abrupt change in electrical voltage or current.
Electrical current or voltage pulses (unipolar) that do not contain high-frequency oscillations are called video pulses (Fig. 2.2). Electrical pulses, which are time-limited high-frequency or ultra-high-frequency electromagnetic oscillations, the envelope of which has the form of a video pulse, are called radio pulses.
According to the nature of the change over time, electrical impulses are distinguished into rectangular, sawtooth, exponential, bell-shaped and other shapes. A real video pulse can have a rather complex shape, which is characterized by amplitude A, pulse duration t And , front duration t f and duration of decline t With , the size of the top chip D A.
Any complex periodic signal can be represented as a sum of harmonious oscillations with frequencies that are multiples of the fundamental frequency.
A non-periodic signal is usually limited in time.
A random signal is a function of time whose values are unknown in advance and can only be predicted with some probability. As the main characteristics random signals accept:
a) the law of probability distribution (the relative time of stay of the signal magnitude in a certain interval);
b) spectral distribution of signal power.
The output signals of the sensors are a reflection of certain physical processes. They tend to be continuous since most physical processes are continuous in nature. Such signals are called analog.
An analog signal is described by a continuous (or piecewise continuous) function x A (t), and the function itself, like its argument, can take any values within specified limits. Analog signals are fairly simple to generate and process, but they can solve relatively simple technical problems. Work of modern electronic systems based on the use of discrete and digital signals.
A discrete time signal is obtained as a result of discretization of a continuous function, which represents the replacement of a continuous function with its instantaneous values at discrete times. Such a signal is described by a lattice function (sequential time series) S(n?t). It can take any values in a certain interval, while the independent variable n takes discrete values n = 0, ±1, ±2,..., and t is the sampling interval.
A signal quantized by level is obtained as a result of the quantization operation. The essence of the level quantization operation is that a number of discrete levels, called quantization levels, are fixed in the continuous dynamic range of an analog signal. The current values of the analog signal are identified with the nearest quantization levels.
Quantization by the level of a discrete time signal allows you to obtain a discretely quantized signal. A digital signal is obtained by numbering the quantization levels of a discretely quantized signal with binary numbers (numbers in the binary number system) and, therefore, representing the sample values of a discretely quantized signal in the form of numbers.
Among deterministic signals A special place is occupied by test signals, the need for the existence of which is determined by the needs of testing the characteristics of developed electronic devices.
Harmonic oscillation. The most common test signal is a harmonic oscillation, which is used in measurement practice to evaluate the frequency properties of devices for various purposes.
A unit step is a dimensionless quantity, so multiplying the signal s(t) by the unit step function is equivalent to turning on this signal at time t=0:
s (t) at t ³ 0;(t) 1 (t) =
at t<t 0.
Delta function. By definition ?-the function satisfies the following conditions:
0 at t¹ t 0;
d(t - t 0) =
At t = t0 ;
Thus, ?-the function is equal to zero for all non-zero values of the argument and takes on an infinitely large value at the point t = 0. Area under a curve bounded ?-function is equal to one.
3. Forms of representation of deterministic signals
Signal models as a function of time are intended primarily for waveform analysis. When solving problems of passing signals of complex shapes through any devices, such a signal model is often not entirely convenient and does not allow one to understand the essence of the physical processes occurring in the devices.
Therefore, signals are represented by a set of elementary (basic) functions, for which orthogonal harmonic (sine and cosine) functions are most often used. The choice of just such functions is due to the fact that they are, from a mathematical point of view, eigenfunctions of time-invariant linear systems (systems whose parameters do not depend on time), i.e. do not change their shape after passing through these systems. As a result, the signal can be represented by a variety of amplitudes, phases and frequencies of harmonic functions, the totality of which is called the signal spectrum.
Thus, there are two forms of representation of an arbitrary deterministic signal: temporal and frequency (spectral).
The first form of representation is based on a mathematical model of the signal as a function of time t:
the second - on the mathematical model of the signal in the form of a function of frequency f, and, which is very important, this model exists only in the field of complex functions:
S = (f) = S(jf).
Both forms of signal representation are interconnected by a pair of Fourier transforms:
When using the angular (cyclic) frequency w = 2pf, the Fourier transforms have the following form:
The time representation of a harmonic oscillation has the following form:
where Um, T, f0, w0, and j0 are the amplitude, period, frequency, angular frequency and initial phase of the oscillation, respectively.
To represent such an oscillation in the frequency domain, it is enough to specify two frequency functions showing that at frequency w0 the signal amplitude is equal to Um and the initial phase is equal to j0:
Graphs of time and frequency representations of harmonic oscillations are shown in Fig. 2.7, where amplitude U m and phase j 0laid out in the form of straight segments.
U values m =U( w 0) And j 0 =j (w 0) are called the amplitude and phase spectrum of a harmonic oscillation, respectively, and their totality is simply a spectrum.
Instead of using two real functions in the frequency domain, you can use a single, but complex function. To do this, we write down the time representation of a harmonic oscillation in complex form:
If we exclude the region of negative frequencies from consideration (they have no physical meaning), then we can write:
Where is the complex amplitude of a harmonic oscillation, the modulus of which is equal to Um, and the argument is j0.
4. Purposes of physical signal processing
The main purpose of processing physical signals is the need to obtain the information contained in them. This information is typically present in the signal amplitude (absolute or relative), frequency or spectral content, phase, or relative timing of multiple 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, format change occurs when transmitting an audio signal 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 cable, or fiber optic cable. In digital communication, analog audio information is first converted into digital by an A/D converter. Digital information representing individual audio channels is time multiplexed (time division multiple access, TDMA) and transmitted over a serial digital link.
Another reason for signal processing is to compress the signal bandwidth (without significant loss of information), followed by formatting and transmission of information at reduced speeds, which allows the required channel bandwidth to be narrowed. In high-speed modems and adaptive pulse code modulation systems, algorithms for eliminating data redundancy (compression) are widely used, as well as in digital mobile communication systems, audio recording systems, and high-definition television.
Hardware and software systems for automating measurements in many cases use information received from sensors to generate appropriate feedback signals, which, in turn, directly control the measurement process. These systems require both ADC and DAC, as well as sensors, signal conditioners and digital processors
In some cases, there is noise in the signal containing information and the main goal is to reconstruct the signal. Techniques such as filtering, synchronous detection, etc. are often used to accomplish this task in both analog and digital domains.
Thus, the objectives of signal conversion are:
· extracting information about the signal (amplitude, phase, frequency, spectral components, time relationships);
· signal format conversion;
·data compression;
· generation of feedback signals;
· analog-to-digital conversion;
· digital-to-analog conversion;
· separating signal from noise.
. Physical signal processing methods
Signals can be processed using:
· analog methods (analog signal processing);
· digital methods (digital signal processing);
· or a combination of analog and digital methods (combined signal processing).
Devices that process analog signals (analog processing) are called analog (analog processors).
Devices that process digital signals (digital processing) are called digital (digital processors).
In some cases, the choice of processing method is clear, in other cases there is no clarity in the choice and, therefore, the final decision is based on certain considerations based on the advantages and disadvantages of the specified methods.
The main advantages of digital signal processing methods include:
· the ability to implement complex signal processing algorithms that are difficult, and often even impossible, to implement using analog technology;
· the ability to implement the principle of “adaptation” or self-tuning, that is, the ability to change the signal processing algorithm without physically restructuring the device (for example, depending on the type of signal entering the filter input);
· possibility of simultaneous processing of several signals;
· fundamentally achievable higher accuracy of signal processing;
· absence of significant influence of instability of parameters of digital processors caused by temperature fluctuations, aging, zero drift, changes in supply voltages and other reasons on the “quality” of signal processing;
· greater noise immunity of digital devices and lower energy, time and frequency “costs” for transmitting digital signals (compared to transmitting analog signals);
· higher level of development of digital devices.
The disadvantages of digital processors include:
· greater complexity compared to analog devices and still higher cost;
· performance is not as high as we would like;
· the inability to eliminate specific errors caused by sampling, signal quantization and rounding during the calculation process.
Today's specialist is faced with choosing the appropriate 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, strain gauges, piezoelectric crystals, disk drive heads, etc.) are analog devices. Therefore, some types of signals require normalization circuits for further signal processing by analog or digital methods. In reality, signal conditioning circuits are analog processors that do:
· amplification of signals in measuring and preliminary (buffer) amplifiers);
· detection of a signal against a background of noise using high-precision common-mode signal amplifiers;
· dynamic range compression (logarithmic amplifiers, logarithmic DACs and programmable gain amplifiers);
· filtration (passive and active).
Literature
1.Volynsky V.A. and others. Electrical engineering / B.A. Volynsky, E.N. Zane, V.E. Shaternikov: Proc. manual for universities. - M.: Energoatomizdat, 2011. - 528 p., ill.
2.Kasatkin A.S., Nemtsov M.V. Electrical engineering: Textbook. manual for universities. - 4th ed., revised. - M.: Energoatomizdat, 2003. - 440 p., ill.
.Fundamentals of Industrial Electronics: Textbook for Non-Electrical Engineering. specialist. universities /V.G. Gerasimov, O M. Knyazkov, A E. Krasnopolsky, V.V. Sukhorukov; edited by V.G. Gerasimova. - 3rd ed., revised. and additional - M.: Higher. school, 2006. - 336 pp., ill.
.Electrical engineering and electronics in 3 books. Ed. V.G. Gerasimova Book 1. Electrical and magnetic circuits. - M.: Higher school. - 2006
.Electrical engineering and electronics in 3 books. Ed. V.G. Gerasimova Book 2. Electromagnetic devices and electrical machines. - M.: Higher school. - 2007
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