Lately, in information network, more and more information began to appear about the transition from analogue to digital broadcasting, in connection with this, many questions arise on this topic, all kinds of rumors and assumptions are generated. In this article, I want to explain what is the difference between "analogue" and "digital" broadcasting in an accessible and understandable language for a simple user (at least as much as possible).

The signals were originally sent on a waveform similar to the original signal, unlike the newer digital signals, which are sent as a binary code. Analog signals were extremely efficient and could be picked up from a great distance, but they also took up a significant amount of bandwidth.

A beam of electrons fired from the back of the tube towards the screen at the front of the tube, illuminating the phosphors on the screen. By modulating the brightness and color-coding the beam, a complete image can be created on the screen. The beam slightly changed the particular image every fraction of a second, tricking your eyes into thinking the image was moving.

First, let's understand what an "analog" signal is.

analog signal

Explain as always, I'll be on simple example. For example, let's take the transmission of voice information from one person to another.

During a conversation, our vocal cords emit a certain vibration of varying pitch (frequency), and loudness (level sound signal). This vibration, having traveled some distance, enters the human ear, acting there, on the so-called auditory membrane. This membrane begins to vibrate with the same frequency and vibration force that our sound cords emitted, with the only difference that the vibration force due to overcoming the distance is somewhat weakened.
So, the transmission of voice speech from one person to another can be safely called
analog signal transmission, and here's why.

Initially, analog televisions were broadcast in black and white, which could be done simply by changing the intensity of the electron beam. When the color arrived, new information was encoded into the signal, allowing the TVs to interpret certain colors. Three main types of color coding have been used.

With the "analog signal", I think, figured it out

In addition, cathode ray tubes required an unwieldy structure to support and were limited to 480 vertical lines to create an image. Here's the good news: An old analog TV will still work with a satellite dish even after a digital conversion.

The point here is that our vocal cords emit the same sound vibration that the human ear itself perceives (we hear what we say), that is, the transmitted and received sound signal has a similar pulse shape, and the same frequency spectrum sound vibrations, or in other words, "analogous" sound vibration.

Install your own satellite dish, or install it yourself, according to the manufacturer's specifications. Connect the satellite to the satellite dish . Connect your subwoofer to your TV. Connect the coaxial wire to the "TV out" port.

Tune your TV to a channel. Call your satellite provider to activate your satellite receiver. Check the purchase of high quality wire; the better the wire, the better picture and sound. Satellite dishSatellite receiverCoaxial wire. . Jack Gorman has been involved in many areas of his professional career. His specialty includes film and video production, sports management, writing, web graphic design, marketing, communications, operations, human resources and photography.

Here, I think it's clear.

Now, let's look at a more complex example. And for this example, let's take a simplified diagram of a telephone set, that is, the phone that people used long before the advent of cellular communications.

During a conversation, speech sound vibrations are transmitted to the sensitive membrane of the handset (microphone). Then, in the microphone, the sound signal is converted into electrical impulses, and then goes through the wires to the second handset, in which, using an electromagnetic transducer (speaker or earphone), the electrical signal is converted back into an audio signal.

Television has developed rapidly over the past decade. Although they are related to each other, they are not exactly the same. It also has the ability to transmit more data in less bandwidth and the ability to broadcast individual sub-channels.

Darrin Mayer has been writing since that time. Meyer holds a Bachelor of Arts degree in broadcast journalism from the University of Nebraska-Lincoln. Well, there is a big difference in quality between the two. The picture quality is far superior to that of digital broadcasting.

A digital image is more accurate because it uses a digital formula to transmit, so you either see the perfect picture or nothing at all. digital system allows more content to be transmitted via radio waves. We definitely live more in the world of computers and technology.

In the example above, again, "analogue" signal conversion is used. That is, the sound vibration has the same frequency as the frequency of the electrical impulse in the communication line, as well as the sound and electrical impulses have a similar shape (that is, similar).

Each station has one frequency on which an analog television signal is broadcast. This can result in static, snow or halo on the channel. It may also cause fluctuations in color, brightness and sound quality. And, like radio signals, analog transmission goes down as farther from the source.

In a digital code, you can encode almost any kind of transmitted electrical signal (including analog), and it doesn’t matter if it’s a picture, video signal, audio signal, or text information, and it is possible to transmit these types of signal almost simultaneously (in a single digital stream).

A digital signal, in terms of its electrical properties (as in the example with a tone signal), has a greater information transmission capacity than an analog signal. Also, a digital signal can be transmitted over a greater distance than an analog one, and without reducing the quality of the transmitted signal.

This means you enjoy consistently crisp images, high-quality audio, and static or snow. Digital transmission requires less bandwidth than a similar analog signal. This allows you to experience quality programming at home. The value of the image is 4 units of width for every 3 units of height.

Unfortunately, television receivers (TVs) designed to receive analog television will no longer be able to receive a digital terrestrial signal. But in any case, this does not mean that you have to go to the store and buy a new TV capable of receiving digital TV.

To enable you to receive digital broadcasting, on a TV that supports only an analog terrestrial signal, you just need to purchase a so-called digital television broadcast receiver (or, in other words, a digital terrestrial receiver).

Digital terrestrial receiver (receiver), connects to the TV through an antenna jack or through a low-frequency audio-video cable. In this case, the terrestrial antenna is no longer connected to the antenna jack of the TV, but to the jack of the digital receiver itself. The general scheme of such a connection is shown in Fig. one.

The general principle of such an approach would be as follows:

The digital terrestrial radio signal will be received by the terrestrial antenna, from the antenna this signal will come to the digital receiver, and from the receiver the analog signal will go to your TV. Here, the TV will already be used as a monitor, and switching between TV channels will occur from the remote control of the digital terrestrial receiver (receiver).

Here I think it should be mentioned, and the reception of sound radio stations.

To receive a digital signal from broadcasting stations, old-style radio receivers (supporting the reception of analog broadcasts) will no longer be suitable, and a special radio receiver is required that supports the reception of a digital radio signal.

Advantages of digital terrestrial TV:

* As mentioned earlier, the main and most important advantage of digital terrestrial TV is, of course, mobility. You can watch your favorite programs not only at home, but also while on the road. Also, perhaps in the future, digital terrestrial TV can be viewed on a mobile phone.
* Digital terrestrial TV, this is the ability to receive images and sound in very good quality.
*According to its electrical properties, or rather electromagnetic properties, a digital signal can be transmitted over a greater distance than an analog signal, and without reducing the quality of the transmitted signal.
Here, it should also be taken into account that the digital radio signal is more resistant to electromagnetic interference around us (interference can come from both nearby electrical and radio devices and nearby power lines).
*V digital format, you can transmit significantly more TV channels, while the quality of the image and sound will be much better than with analog signal transmission.
* The undoubted advantage of digital terrestrial broadcasting is, of course, ease of setup, while, for example, installing and configuring satellite television requires certain knowledge and skills.

I think this, of course, is not the whole list of advantages of digital broadcasting over analog broadcasting, but, as they say, we'll wait and see.

Digital television is rapidly gaining popularity in our country, but many people still do not know how it is fundamentally different from the good old analog TV.

Description of analog and digital television

It is not difficult to guess that the basis of analog and digital television are analog and digital signals, respectively. The analog signal is continuous, which means that in the event of any influence from the outside, it is vulnerable, which leads to poorer picture and sound quality. The undoubted advantage of the analog signal is the ability to receive it using a simple terrestrial antenna. You can also use the services of a cable TV provider. It can be said that the analog signal is already obsolete today, since it is significantly inferior to the digital signal in a number of important parameters - quality, safety, etc.
Modern televisions are designed primarily to work with a digital signal, although they also have an analog connector. It's just that the analog signal is not able to reveal the full potential of modern plasma and LCD TVs, only a digital signal can give the best picture quality. It, unlike analog, comes in compact “portions”, which are separated by pauses, and therefore it is very difficult to influence such a signal. Even when transmitting a digital signal over a very long distance, the picture and sound quality remains at the highest level. Among other things, a digital signal allows you to transmit much more channels than an analog signal, so subscribers who connect digital television receive more than a hundred TV channels on a wide variety of topics.

Comparison of analog and digital television

Alas, analog television today actually has no clear advantages over digital broadcasting, except perhaps the ability to "catch" the signal using a conventional antenna. However, digital television can also be mobile using a digital signal receiver. Considering that regardless of the distance, the digital signal remains protected from hacking and interference and guarantees high level quality, the advantages of digital television are becoming quite obvious.

TheDifference.ru determined that the difference between analogue and digital television is as follows:

Digital television provides a higher level of signal quality and protection. The analog signal was and remains vulnerable to external influences and cannot provide such a high-quality image.
Digital television is more mobile - today you can already receive a digital signal while on the road or far from home.
Analog TV is unable to provide such a large number channels like digital. Due to the peculiarities of the digital signal, when connecting digital TV, the subscriber can get access to several hundred different TV channels.

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When dealing with television and radio broadcasting, as well as modern types of communications, you often come across terms such as "analog signal" and "digital signal". For specialists, there is no mystery in these words, but for ignorant people, the difference between “digital” and “analogue” may be completely unknown. And yet there is a very significant difference.

When we talk about a signal, we usually mean electromagnetic oscillations that induce an EMF and cause current fluctuations in the receiver antenna. Based on these fluctuations, the receiving device - a TV, radio, walkie-talkie or cell phone - makes up an “idea” about what image to display on the screen (if there is a video signal) and what sounds to accompany this video signal.

In any case, the signal of the radio station or tower mobile communications can appear in both digital and analog form. After all, for example, the sound itself is an analog signal. At the radio station, the sound perceived by the microphone is converted into the already mentioned electromagnetic oscillations. The higher the sound frequency, the higher the oscillation frequency at the output, and the louder the speaker speaks, the greater the amplitude.

The resulting electromagnetic oscillations, or waves, propagate in space with the help of a transmitting antenna. So that the air is not clogged with low-frequency interference, and so that different radio stations have the opportunity to work in parallel without interfering with each other, the vibrations resulting from the impact of sound are summarized, that is, they are “superimposed” on other vibrations that have a constant frequency. The last frequency is usually called the "carrier", and it is on its perception that we tune our radio receiver in order to "catch" the analog signal of the radio station.

In the receiver, the reverse process occurs: the carrier frequency is separated, and the electromagnetic oscillations received by the antenna are converted into sound oscillations, and the familiar voice of the announcer is heard from the speaker.

In the process of transmitting an audio signal from a radio station to a receiver, anything can happen. Third-party interference may occur, the frequency and amplitude may change, which, of course, will be reflected in the sounds emitted by the radio. Finally, both the transmitter and receiver themselves introduce some error during signal conversion. Therefore, the sound reproduced by an analog radio always has some distortion. The voice may be perfectly reproduced, despite the changes, but there will be hissing or even some kind of wheezing caused by interference in the background. The less confident the reception, the louder and more distinct these extraneous noise effects will be.

In addition, the over-the-air analog signal has a very weak degree of protection against unauthorized access. For public radio stations, this, of course, does not matter. But while using the first mobile phones there was one unpleasant moment associated with the fact that almost any outside radio could be easily tuned to the right wave to eavesdrop on your telephone conversation.

Analog broadcasting has such shortcomings. Because of them, for example, television promises to become completely digital in a relatively short time.

Digital communications and broadcasting are considered to be more immune to interference and external influences. The thing is that when using the "numbers" the analog signal from the microphone at the transmitting station is encrypted into a digital code. No, of course, the flow of figures and numbers does not spread into the surrounding space. It's just that the sound of a certain frequency and volume is assigned a code from radio pulses. The duration and frequency of the pulses are set in advance - it is the same for both the transmitter and the receiver. The presence of a pulse corresponds to one, the absence corresponds to zero. Therefore, such a connection is called "digital".

A device that converts an analog signal into a digital code is called analog-to-digital converter (ADC). And a device installed in the receiver that converts the code into an analog signal corresponding to the voice of your friend in the speaker cell phone GSM standard is called a "digital-to-analog converter" (DAC).

During the transmission of a digital signal, errors and distortions are practically excluded. If the impulse becomes a little stronger, longer, or vice versa, then it will still be recognized by the system as a unit. And zero will remain zero, even if some random weak signal. For ADC and DAC, there are no other values, like 0.2 or 0.9 - only zero and one. Therefore, interference on digital communications and broadcasting has almost no effect.

Moreover, the “digit” is also more protected from unauthorized access. Indeed, in order for the DAC of the device to be able to decrypt the signal, it is necessary that it “know” the decryption code. The ADC, along with the signal, can also transmit the digital address of the device selected as the receiver. Thus, even if the radio signal is intercepted, it cannot be recognized due to the absence of at least part of the code. This is especially true.

So, here differences between digital and analog signals:

1) An analog signal can be distorted by interference, and a digital signal can either be completely jammed with interference, or come without distortion. A digital signal is either exactly there, or completely absent (either zero or one).

2) The analog signal is available for perception by all devices operating on the same principle as the transmitter. The digital signal is securely coded and hard to intercept if it's not intended for you.

An analog signal is a function of a continuous argument (time). If the graph is periodically interrupted, as happens in a sequence of pulses, for example, they are already talking about a certain discreteness of the pack.

The history of the term

Computer Engineering

If you read carefully, it is not written anywhere where the definition came from - analog. In the West, the term has been used since the forties by professionals computer science. It was during the Second World War that the first computer systems called digital. And for the distinction had to come up with new epithets.

To the world household appliances the concept of analog entered only in the early 80s, when the first Intel processors, and the world was playing with toys on the ZX-Spectrum, an emulator for devices today can be obtained on the Internet. The gameplay required extraordinary perseverance, skill and excellent reaction. Along with the children, they collected boxes and beaten enemy aliens and adults. Modern games are far inferior to the first birds that captured the minds of the players for a while.

Sound recording and telephony

By the beginning of the 1980s, pop music in electronic processing began to appear. The musical telegraph was presented to the public in 1876, but did not gain recognition. Popular music likes the audience in the broadest sense of the word. The telegraph was able to issue a single note, transmit it to a distance where it was reproduced by a speaker of a special design. And although the Beatles used an electronic organ to create Sergeant Pepper, the synthesizer came into use in the late 70s. A truly popular and digital tool became already in the mid-80s: remember Modern Talking. Previously, synthesizers were used on analog circuits starting with Novachord in 1939.

So, the need to distinguish between analog and digital technologies the ordinary citizen did not arise until the latter became firmly established in everyday life. The word analog has been in the public domain since the early 80s. As for the origin of the term, it is traditionally believed that the pointer was borrowed from telephony, later migrated to sound recording. Analog vibrations are directly fed to the speaker, and the voice is immediately heard. The signal is similar to human speech, becomes an electrical analogue.

If you apply a digital signal to the speaker, an indescribable cacophony of notes of different keys will be heard. This "speech" is familiar to anyone who has loaded programs and games from magnetic tape into the computer's memory. It doesn't look like a human, because it's digital. As for the discrete signal, in the simplest systems it is fed directly to the speaker, which serves as an integrator. The success or failure of an enterprise depends entirely on the right parameters.

At the same time, the term appeared in sound recordings, where music and voice went directly from the microphone to the tape. Magnetic recording has become an analogue of real artists. Vinyl records are like musicians and are still considered the best medium for any composition. Although they show a limited service life. CDs now often contain digital sound decoded by the decoder. According to Wikipedia, a new era began in 1975 (en.wikipedia.org/wiki/History_of_sound_recording).

Electrical measurements

V analog signal there is a proportionality between the voltage or current and the response on the reproducing device. The term is then considered to be derived from the Greek analogos. What does proportional mean. However, the comparison is similar to the one above: the signal is similar to the voice reproduced by the speakers.

In addition, in technology, another term is used to refer to analog signals - continuous. Which corresponds to the above definition.

general information

Signal energy

As follows from the definition, an analog signal has infinite energy and is not limited in time. Therefore, its parameters are averaged. For example, 220 V present at the outlet is called RMS for the reason indicated. Therefore, effective (averaged over a certain interval) values ​​are used. It is already clear that there is an analog signal with a frequency of 50 Hz in the outlet.

When it comes to discreteness, finite values ​​are used. For example, when buying a stun gun, you need to make sure that the impact energy does not exceed a particular value, measured in joules. Otherwise, there will be trouble with the use or during the inspection. Since, starting from a specific energy value, the stun gun is used only by special forces, with an established upper limit. Others are illegal in principle, capable of causing death when used.

The pulse energy is found by multiplying the current and voltage by the duration. And this shows the finiteness of the parameter for discrete signals. In technology, there are also digital sequences. It differs from a discrete digital signal by hard-coded parameters:

1. duration.
2. Amplitude.
3. The presence of two given states: 0 and 1.
4. Machine bits 0 and 1 are added to the words agreed in advance and understood by the participants (assembly language).

Mutual conversion of signals

An additional definition of an analog signal is its apparent randomness, lack of visible rules, or similarity with some natural processes. For example, a sinusoid can describe the rotation of the Earth around the Sun. This is an analog signal. In the theory of circuits and signals, a sinusoid is represented by a rotating amplitude vector. And the phase of current and voltage is different - these are two different vectors, giving rise to reactive processes. What is observed in inductors and capacitors.

It follows from the definition that an analog signal is easily converted into a discrete one. Any impulse block power cuts the input voltage from the outlet into packs. Therefore, it is engaged in the conversion of an analog signal of a frequency of 50 Hz into discrete ultrasonic bursts. By varying the slicing parameters, the power supply adjusts the output values ​​to the requirements of the electrical load.

Inside the receiver of radio waves with an amplitude detector, the reverse process occurs. After the signal is rectified, pulses of various amplitudes are formed on the diodes. The information is embedded in the envelope of such a signal, the line connecting the peaks of the message. The filter is engaged in the conversion of discrete pulses into an analog value. The principle is based on the integration of energy: during the period of voltage, the charge of the capacitor increases, then, in the interval between the peaks, the current is formed due to the previously accumulated supply of electrons. The resulting wave is fed to a low-frequency amplifier, later to speakers, where the result is heard by others.

The digital signal is encoded differently. There, the amplitude of the pulse is embedded in the machine word. It consists of ones and zeros, decoding is required. The operation is being carried out electronic devices: graphics adapter, software products. Everyone downloaded K-Lite codecs from the Internet, this is the case. The driver is engaged in decoding the digital signal and converting it for output to speakers and a display.

No need to rush into confusion when an adapter is called a 3-D accelerator and vice versa. The first only converts the given signal. For example, for digital input DVI is always an adapter. It deals only with the conversion of numbers from ones and zeros for display on the screen matrix. Retrieves information about brightness and RGB pixel values. As for the 3D accelerator, the device may (but is not required) to contain an adapter, but the main task is complex calculations for the construction of three-dimensional images. This technique allows you to unload the central processor and speed up the work of a personal computer.

From analog to digital signal is converted to ADC. This happens programmatically or inside the microcircuit. Separate systems combine both methods. The procedure begins by taking readings that fit inside the specified area. Each, being transformed, becomes a machine word containing the calculated figure. Then the readings are packed in parcels, it becomes possible to send a complex system to other subscribers.

The sampling rules are normalized by the Kotelnikov theorem, which shows the maximum frequency of sampling. More often, it is forbidden to take a reading, since information is lost. Simplistically, a sixfold excess of the sampling rate over the upper limit of the signal spectrum is considered sufficient. More stock is considered an added benefit, guaranteeing good quality. Anyone has seen indications of the sampling rate of audio recordings. Usually the setting is above 44 kHz. The reason is the peculiarities of human hearing: the upper limit of the spectrum is 10 kHz. Therefore, a sampling frequency of 44 kHz is enough for a mediocre sound transmission.

Difference between discrete and digital signal

Finally, a person from the surrounding world usually perceives analog information. If the eye sees a flashing light, the peripheral vision will capture the surrounding landscape. Therefore, the final effect is not seen as discrete. Of course, it is possible to try to create a different perception, but this is difficult and will turn out to be completely artificial. This is the basis for the use of Morse code, which consists of dots and dashes that are easily distinguishable against the background of noise. Discrete strokes of the telegraph key are difficult to confuse with natural signals, even in the presence of strong noise.

The same way digital lines introduced in technology to eliminate interference. Any video lover is trying to get their hands on an encoded copy of the movie in the highest resolution. Digital information is capable of being transmitted over long distances without the slightest distortion. The rules known on both sides for the formation of prearranged words become helpers. Sometimes redundant information is embedded in a digital signal, allowing you to correct or notice errors. This eliminates misperception.

Pulse signals

To be more precise, discrete signals are given by counts at certain points in time. It is clear that such a sequence is not formed in reality due to the fact that the front and recession have a finite length. The impulse is not transmitted instantly. Therefore, the spectrum of the sequence is not considered discrete. So the signal can't be called that. In practice, there are two classes:

1. Analog pulse signals - the spectrum of which is found by the Fourier transform, therefore, continuous, at least in certain areas. The result of the action of voltage or current on the circuit is found by the convolution operation.
2. Discrete pulse signals also show a discrete spectrum, operations with them are carried out through discrete Fourier transforms. Therefore, discrete convolution is also applied.

These clarifications are important for literalists who have read that pulsed signals are analog. Discrete are named after the features of the spectrum. The term analog is used to distinguish. The epithet continuous is applicable, as already mentioned above, and in connection with the features of the spectrum.

Clarification: only the spectrum of an infinite sequence of pulses is considered strictly discrete. For a pack, the harmonic components are always vague. Such a spectrum resembles a sequence of pulses modulated in amplitude.

The layman does not think about the nature of the signals, but sometimes it is necessary to think about the difference between analog and digital broadcasting or formats. By default, it is considered that analog technologies are becoming a thing of the past, and will soon be completely replaced by digital ones. It is worth knowing what we are giving up in favor of new trends.

analog signal is a data signal described by continuous functions of time, that is, its oscillation amplitude can take any value within the maximum.

digital signal is a data signal described by discrete functions of time, that is, the oscillation amplitude takes on only strictly defined values.

In practice, this allows us to say that the analog signal is accompanied by a large amount of interference, while the digital one successfully filters them out. The latter is able to restore the original data. In addition, a continuous analog signal often carries a lot of unnecessary information, which leads to its redundancy - several digital signals can be transmitted instead of one analog signal.

If we talk about television, and it is this area that worries most consumers with its transition to digital, then we can consider the analog signal to be completely obsolete. However, for the time being, any equipment designed for this purpose accepts analog signals, and digital requires a special one. True, with the spread of “digits” there are fewer and fewer analog TVs and the demand for them is drastically decreasing.

One more important characteristic signal - safety. In this respect, analog shows complete vulnerability to outside influences or intrusions. Digital is encrypted by assigning it a code from radio pulses, so that any interference is excluded. It is difficult to transmit digital signals over long distances, therefore a modulation-demodulation scheme is used.

Findings site

1. The analog signal is continuous, the digital signal is discrete.
2. When transmitting an analog signal, the risk of clogging the channel with interference is higher.
3. The analog signal is redundant.
4. The digital signal filters the noise and restores the original data.
5. The digital signal is transmitted in encrypted form.
6. Multiple digital signals can be sent instead of one analog signal.

Analogue, Discrete and Digital Signals

INTRODUCTION TO DIGITAL SIGNAL PROCESSING

Digital signal processing (DSP or DSP - digital signal processing) is one of the latest and most powerful technologies that is being actively implemented in a wide range of fields of science and technology, such as communications, meteorology, radar and sonar, medical imaging, digital audio and television broadcasting, exploration of oil and gas fields, etc. We can say that there is a widespread and deep penetration of technologies digital processing signals to all spheres of human activity. Today, DSP technology is one of the basic knowledge that scientists and engineers need in all industries without exception.

Signals

What is a signal? In the most general formulation, this is the dependence of one quantity on another. That is, from a mathematical point of view, the signal is a function. Most often, time dependencies are considered. The physical nature of the signal can be different. Very often it is an electric voltage, less often it is a current.

Waveforms:

1. temporary;

2. spectral (in the frequency domain).

The cost of digital data processing is less than analog and continues to decline, while the performance of computing operations is constantly increasing. It is also important that DSP systems are highly flexible. They can be supplemented with new programs and reprogrammed to perform various operations without changing the equipment. Therefore, interest in scientific and applied issues of digital signal processing is growing in all branches of science and technology.

FOREWORD TO DIGITAL SIGNAL PROCESSING

Discrete signals

The essence of digital processing is that physical signal (voltage, current, etc.) is converted into a sequence numbers, which is then subjected to mathematical transformations in the WT.

Analogue, Discrete and Digital Signals

The original physical signal is a continuous function of time. Such signals defined at all times t are called analog.

What is a digital signal? Consider some analog signal (Fig. 1.1 a). It is set continuously over the entire time interval under consideration. The analog signal is considered to be absolutely accurate, if you do not take into account the errors in the measurement.

Rice. 1.1 a) Analog signal

Rice. 1.1 b) Sampled signal

Rice. 1.1 c) Quantized signal

To receive you need to digital signal, you need to perform two operations - discretization and quantization. The process of converting an analog signal into a sequence of samples is called discretization, and the result of this transformation is discrete signal.T. arr., sampling consists in drawing up a sample from an analog signal (Fig. 1.1 b), each element of which, called countdown, will be separated in time from neighboring samples on a certain interval T called sampling interval or (because the sampling interval is more often unchanged) - sampling period. The reciprocal of the sampling period is called sample rate and is defined as:

(1.1)

When processing a signal in a computing device, its readings are presented in the form binary numbers having limited number discharges. As a result, samples can take only a finite set of values ​​and, therefore, when the signal is presented, it inevitably rounds off. The process of converting signal samples into numbers is called quantization. The resulting rounding errors are called rounding errors or quantization noise. Thus, quantization is the reduction of the levels of the sampled signal to a certain grid (Fig. 1.1 c), more often by the usual rounding up. A signal that is discrete in time and quantized in terms of level will be digital.

The conditions under which it is possible to completely restore an analog signal from its digital equivalent while preserving all the information originally contained in the signal are expressed by the Nyquist, Kotelnikov, Shannon theorems, the essence of which is almost the same. To sample an analog signal with full preservation of information in its digital equivalent, the maximum frequencies in the analog signal must be at least half the sampling rate, that is, f max £ (1/2)f d , i.e. on one period maximum frequency There must be at least two counts. If this condition is violated, the effect of masking (substitution) of real frequencies by lower frequencies occurs in the digital signal. In this case, the "apparent" frequency is recorded in the digital signal instead of the actual one, and, consequently, the restoration of the actual frequency in the analog signal becomes impossible. The reconstructed signal will look as if the frequencies above half the sampling frequency are reflected from the frequency (1/2)f d to the lower part of the spectrum and superimposed on the frequencies already present in this part of the spectrum. This effect is called aliasing or aliasing(aliasing). An illustrative example of aliasing is an illusion that is quite common in movies - the wheel of a car starts to rotate against its movement if between successive frames (sampling frequency analog) the wheel makes more than half a turn.

Signal conversion to digital form performed by analog-to-digital converters (ADCs). Typically they use binary system reckoning with a certain number of digits in a uniform scale. Increasing the number of digits improves measurement accuracy and extends dynamic range measured signals. The information lost due to the lack of ADC bits is unrecoverable, and there are only estimates of the resulting error in the “rounding off” of readings, for example, through the noise power generated by an error in the last ADC bit. For this, the concept of the signal-to-noise ratio is used - the ratio of signal power to noise power (in decibels). The most commonly used are 8-, 10-, 12-, 16-, 20- and 24-bit ADCs. Each additional shock improves the signal-to-noise ratio by 6 decibels. However, increasing the number of bits reduces the sampling rate and increases the cost of the hardware. An important aspect is also the dynamic range, which is determined by the maximum and minimum values ​​of the signal.

Digital Signal Processing either special processors, or on mainframes and computers by special programs. The easiest to consider linear systems. Linear called systems for which the principle of superposition takes place (the response to the sum of input signals is equal to the sum of the responses to each signal separately) and uniformity (a change in the amplitude of the input signal causes a proportional change in the output signal).

If the input signal x(t-t 0) generates an unambiguous output signal y(t-t 0) at any shift t 0 , then the system is called time invariant. Its properties can be explored at any arbitrary times. To describe the linear system, a special input signal is introduced - single impulse(impulse function).

Single impulse(single count) u 0(n) (Fig. 1.2):

Rice. 1.2. Single impulse

Due to the properties of superposition and homogeneity, any input signal can be represented as the sum of such pulses applied at different times and multiplied by the appropriate coefficients. The output signal of the system in this case is the sum of the responses to these pulses. The response to a single pulse (pulse with a unit amplitude) is called system impulse responseh(n). Knowledge of the impulse response makes it possible to analyze the passage of any signal through a discrete system. Indeed, an arbitrary signal (x(n)) can be represented as a linear combination of unit samples.