An analog signal is a data signal in which each of the representing parameters is described by a function of time and a continuous set of possible values.

There are two signal spaces - the space L (continuous signals), and the space l (L is small) - the space of sequences. The space l (L is small) is the space of the Fourier coefficients (a countable set of numbers that define a continuous function on a finite interval of the domain of definition), the space L is the space of continuous signals in the domain of definition. Under certain conditions, the space L is uniquely mapped to the space l (for example, the first two Kotelnikov discretization theorems).

Analog signals are described by continuous functions of time, therefore analog signal sometimes referred to as continuous beep. Analog signals are opposed to discrete (quantized, digital). Examples of continuous spaces and corresponding physical quantities:

direct: electrical voltage

circumference: the position of the rotor, wheel, gears, analog clock hands, or the phase of the carrier signal

segment: position of the piston, control lever, liquid thermometer or electrical signal, limited in amplitude various multidimensional spaces: color, quadrature modulated signal.

The properties of analog signals are largely the opposite of those of quantized or digital signals.

The lack of clearly distinguishable from each other discrete signal levels leads to the impossibility of applying the concept of information to its description in the form as it is understood in digital technologies. The "amount of information" contained in one sample will be limited only by the dynamic range of the measuring instrument.

No redundancy. From the continuity of the value space, it follows that any interference introduced into the signal is indistinguishable from the signal itself and, therefore, the original amplitude cannot be restored. In fact, filtering is possible, for example, by frequency methods, if any additional information about the properties of this signal is known (in particular, the frequency band).

Application:

Analog signals are often used to represent continuously changing physical quantities. For example, an analog electrical signal taken from a thermocouple carries information about temperature changes, a signal from a microphone - about rapid pressure changes in a sound wave, etc.

2.2 Digital signal

Digital signal is a data signal in which each of the representing parameters is described by a discrete time function and a finite set of possible values.

Signals are discrete electrical or light pulses. With this method, the entire capacity of the communication channel is used to transmit one signal. The digital signal uses the entire bandwidth of the cable. Bandwidth is the difference between the maximum and minimum frequency that can be transmitted over the cable. Each device in such networks sends data in both directions, and some can simultaneously receive and transmit. Baseband systems transmit data as a digital signal of a single frequency.

A discrete digital signal is more difficult to transmit over long distances than an analog signal, therefore it is pre-modulated on the transmitter side, and demodulated on the information receiver side. The use of algorithms for checking and restoring digital information in digital systems can significantly increase the reliability of information transmission.

Comment. It should be borne in mind that a real digital signal is analog by its physical nature. Due to noise and changes in the parameters of transmission lines, it has fluctuations in amplitude, phase / frequency (jitter), polarization. But this analog signal (pulse and discrete) is endowed with the properties of a number. As a result, it becomes possible to use numerical methods for its processing (computer processing).

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

Analog signal- a data signal described by continuous functions of time, that is, its oscillation amplitude can take any values ​​within the maximum.

Digital signal- a data signal described by discrete functions of time, that is, the amplitude of oscillations takes on values ​​only strictly defined.

In practice, this allows us to say that the analog signal is accompanied by a large amount of noise, while the digital signal 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.

If we talk about television, and it is this sphere that worries most consumers with its transition to “digital”, then the analog signal can be considered completely obsolete. However, so far, analog signals are received by any equipment intended for this, and digital requires a special one. True, with the spread of "numbers" analog TVs less and less and the demand for them is dramatically decreasing.

Another important signal characteristic is safety. In this respect, analog demonstrates complete defenselessness against influences or intrusions from the outside. The digital one is encrypted by assigning a code to it 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.

Conclusions 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 noise is higher.
3. The analog signal is redundant.
4. The digital signal filters noise and recovers the original data.
5. The digital signal is transmitted encrypted.
6. Several digital signals can be sent instead of one analog signal.

The average consumer does not need to know what the nature of the signals is. But sometimes it is necessary to know the difference between analog and digital formats in order to approach the choice of one or another option with open eyes, because today it is rumored that the time of analog technologies has passed, they are being replaced by digital ones. You should understand the difference in order to know what we are leaving and what to expect.

Analog signal is a continuous signal with an infinite number of data close in value within the maximum, all parameters of which are described by a time dependent variable.

Signal digital- this is a separate signal, described by a separate function of time, respectively, at each moment of time, the magnitude of the signal amplitude has a strictly defined value.

Practice has shown that with analog signals, interference is possible that can be eliminated with a digital signal. In addition, digital can recover the original data. With a continuous analog signal, a lot of information passes through, often unnecessary. Instead of one analog, several digital ones can be transmitted.

Today, the consumer is interested in the issue of television, since it is in this context that the phrase "transition to digital signal". In this case, analog can be considered a relic of the past, but it is precisely it that is accepted by the existing technology, and for digital reception, a special one is needed. Of course, in connection with the emergence and expansion of the use of" numbers ", they are losing their former popularity.

Advantages and disadvantages of signal types

Safety plays an important role in assessing the parameters of a particular signal. Various influences, intrusions make the analog signal defenseless. With digital, this is excluded, since it is encoded from radio pulses. For long distances, the transmission of digital signals is complicated, it is necessary to use modulation-demodulation schemes.

Summing up, we can say that differences between analog and digital signal consist of:

• In the continuity of the analog and the discreteness of the digital;
• More likely to interfere with analog transmission;
• The redundancy of the analog signal;
• In the ability to digitally filter noise and recover the original information;
• In the transmission of a digital signal in coded form. One analog signal is replaced by several digital ones.

Very often we hear such definitions as “digital” or “discrete” signal, how is it different from “analog”?

The difference is that the analog signal is continuous in time (blue line), while the digital signal consists of a limited set of coordinates (red dots). If everything is reduced to coordinates, then any segment of an analog signal consists of an infinite number of coordinates.

For a digital signal, the coordinates along the horizontal axis are located at regular intervals, in accordance with the sampling frequency. In the common Audio-CD format, this is 44,100 dots per second. Vertically, the accuracy of the coordinate height corresponds to the digit capacity of the digital signal, for 8 bits it is 256 levels, for 16 bits = 65536 and for 24 bits = 16777216 levels. The higher the bit depth (number of levels), the closer the vertical coordinates to the original wave.

Analogue sources are vinyl and audio tapes. Digital sources are: CD-Audio, DVD-Audio, SA-CD (DSD) and files in WAVE and DSD formats (including derivatives of APE, Flac, Mp3, Ogg, etc.).

Analog Signal Advantages and Disadvantages

The advantage of the analog signal is that it is in the analog form that we perceive sound with our ears. And although our auditory system converts the perceived sound stream into digital form and transfers it in this form to the brain, science and technology have not yet reached the possibility of connecting players and other sound sources directly in this form. Such research is now actively conducted for people with disabilities, and we enjoy exclusively analog sound.

The disadvantage of an analog signal is the ability to store, transmit and replicate the signal. When recording to tape or vinyl, the signal quality will depend on the properties of the tape or vinyl. Over time, the tape will demagnetize and the quality of the recorded signal will deteriorate. Each read gradually destroys the medium, and rewriting introduces additional distortion, where additional deviations are added by the next medium (tape or vinyl), devices for reading, recording and transmitting a signal.

To make a copy of an analog signal is like taking another photograph to copy a photograph.

Advantages and Disadvantages of a Digital Signal

The advantages of a digital signal include accuracy when copying and transmitting an audio stream, where the original is no different from the copy.

The main disadvantage can be considered that the digital signal is an intermediate stage and the accuracy of the final analog signal will depend on how detailed and accurately the coordinates of the sound wave will be described. It is quite logical that the more points there are and the more accurate the coordinates are, the more accurate the wave will be. But there is still no consensus on how many coordinates and data accuracy are sufficient to say that the digital representation of the signal is sufficient to accurately reconstruct the analog signal, indistinguishable from the original by our ears.

In terms of data volumes, the capacity of a conventional analog audio cassette is only about 700-1.1 MB, while a regular CD holds 700 MB. This gives an indication of the need for high-capacity media. And this gives rise to a separate war of compromises with different requirements for the number of describing points and the accuracy of coordinates.

Today it is considered quite sufficient to represent a sound wave with a sampling rate of 44.1 kHz and a bit depth of 16 bits. With a sampling rate of 44.1 kHz, you can recover up to 22 kHz. As psychoacoustic studies show, a further increase in the sampling rate is little noticeable, but an increase in bit depth gives a subjective improvement.

How DACs Build the Wave

A DAC is a digital-to-analog converter, an element that converts digital sound into analog. We will take a quick look at the basic principles. If the comments show interest to consider a number of points in more detail, then a separate material will be released.

Multibit DACs

Very often, the wave is presented in the form of steps, which is due to the architecture of the first generation of multibit R-2R DACs, which operate in a similar way to a switch from a relay.

The DAC input receives the value of the next coordinate along the vertical and in each of its cycles it switches the current (voltage) level to the corresponding level until the next change.

Although it is believed that the human ear hears no more than 20 kHz, and according to Nyquist theory it is possible to restore a signal up to 22 kHz, the question of the quality of this signal after restoration remains. In the high frequency region, the shape of the resulting "step" wave is usually far from the original one. The easiest way out of the situation is to increase the sampling rate when recording, but this leads to a significant and unwanted increase in the file size.

An alternative option is to artificially increase the sampling rate during playback in the DAC by adding intermediate values. Those. we represent the path of a continuous wave (gray dotted line), smoothly connecting the original coordinates (red points) and add intermediate points on this line (dark purple).

When increasing the sampling rate, it is usually necessary to increase the bit depth so that the coordinates are closer to the approximated wave.

Thanks to intermediate coordinates, it is possible to reduce the "steps" and build the wave closer to the original.

When you see a 44.1 to 192 kHz boost function in a player or external DAC, it’s a function to add intermediate coordinates, not restore or create sound in the region above 20 kHz.

Initially, these were separate SRC microcircuits before the DAC, which then migrated directly to the DAC microcircuits themselves. Today you can find solutions where such a microcircuit is added to modern DACs, this is done in order to provide an alternative to the built-in algorithms in the DAC and sometimes get even more best sound(as for example it is done in Hidizs AP100).

The main refusal in the industry from multi-bit DACs occurred due to the impossibility of further technological development of quality indicators with current production technologies and a higher cost versus "pulse" DACs with comparable characteristics. Nevertheless, in Hi-End products, preference is often given to old multi-bit DACs, rather than new solutions with technically better characteristics.

Pulse DAC

In the late 70s, an alternative version of DACs based on a "pulse" architecture - "delta-sigma", became widespread. Pulse DAC technology made possible the emergence of ultra-fast switches and allowed the use of a high carrier frequency.

The signal amplitude is the average value of the pulse amplitudes (pulses of equal amplitude are shown in green, and the final sound wave is shown in white).

For example, a sequence of eight clock cycles of five pulses will give an average amplitude (1 + 1 + 1 + 0 + 0 + 1 + 1 + 0) / 8 = 0.625. The higher the carrier frequency, the more pulses will be smoothed and the more accurate the amplitude will be. This made it possible to present the audio stream in one-bit form with a wide dynamic range.

Averaging can be done as usual analog filter and if such a set of impulses is applied directly to the speaker, then at the output we will get sound, and ultra high frequencies will not be reproduced due to the large inertness of the emitter. PWM amplifiers in class D work according to this principle, where the energy density of the pulses is created not by their number, but by the duration of each pulse (which is easier to implement, but cannot be described with a simple binary code).

A multi-bit DAC can be thought of as a printer capable of applying color with pantone inks. Delta-Sigma is an inkjet printer with a limited set of colors, but due to the ability to apply very small dots (in comparison with an antler printer), due to the different density of dots per unit surface, it gives more shades.

In the image, we usually do not see individual points due to the low resolution of the eye, but only the middle tone. Likewise, the ear does not hear the impulses separately.

Ultimately, with current technologies in pulse DACs, you can get a wave close to the one that theoretically should be obtained when approximating intermediate coordinates.

It should be noted that after the appearance of the delta-sigma DAC, the urgency to draw a "digital wave" with steps has disappeared, since so modern DACs do not build a wave with steps. Correctly construct a discrete signal with points connected by a smooth line.

Are switching DACs ideal?

But in practice, not everything is cloudless, and there are a number of problems and limitations.

Because the overwhelming number of records are stored in a multi-bit signal, then conversion into a pulse signal according to the “bit-for-bit” principle requires an unnecessarily high carrier frequency, which modern DACs do not support.

The main function of modern pulse DACs is to convert a multi-bit signal into a one-bit one with a relatively low carrier frequency with data decimation. Basically, it is these algorithms that determine the final sound quality of impulse DACs.

To reduce the problem of a high carrier frequency, the audio stream is split into several one-bit streams, where each stream is responsible for its own group of discharge, which is equivalent to a multiple increase in the carrier frequency of the number of streams. These DACs are called multi-bit delta-sigma DACs.

Pulse DACs have received a second wind in high-speed microcircuits today. general purpose in the products of NAD and Chord companies due to the ability to flexibly program transformation algorithms.

DSD format

After the widespread use of delta-sigma DACs, the appearance of the recording format was quite logical. binary code directly delta-sigma encoded. This format is called DSD (Direct Stream Digital).

The format was not widely used for several reasons. Editing files in this format turned out to be unnecessarily limited: you cannot mix streams, adjust the volume and apply equalization. This means that without loss of quality, you can only archive analog recordings and make a two-microphone recording of live performances without further processing. In a word, you can't really make money.

In the fight against piracy, SA-CDs were not supported (and are not supported until now) by computers, which prevents them from making copies. No copies - no general audience. It was possible to play DSD audio content only from a separate SA-CD player from a branded disc. If for the PCM format there is an SPDIF standard for digital transmission of data from a source to a separate DAC, then there is no standard for the DSD format and the first pirated copies of SA-CD discs were digitized from the analog outputs of SA-CD players (although the situation seems silly, but in reality some recordings were released only on SA-CD, or the same recording on Audio-CD was specially made poorly to promote SA-CD).

The turning point occurred with the release of the SONY game consoles, where the SA-CD was automatically copied to HDD prefixes. Fans of the DSD format took advantage of this. The advent of pirated recordings stimulated the market to release separate DACs for playing DSD streams. Most external DACs with DSD support today support USB data transfer using the DoP format as a separate digital signal encoding over SPDIF.

The carrier frequencies for DSD are relatively small, 2.8 and 5.6 MHz, but this audio stream does not require any decimation conversions and is quite competitive with high-definition formats such as DVD-Audio.

There is no definite answer to the question of which is better, DSP or PCM. Everything rests on the quality of the implementation of a specific DAC and the talent of the sound engineer when recording the final file.

General conclusion

Analog sound is what we hear and perceive as the world around us with our eyes. Digital sound is a set of coordinates that describe a sound wave, and which we cannot directly hear without converting it into an analog signal.

An analog signal recorded directly onto an audio tape or vinyl cannot be re-recorded without loss of quality, while a wave in digital form can be copied bit by bit.

Digital recording formats are a constant trade-off between the amount of coordinate accuracy versus file size, and any digital signal is only an approximation to the original analog signal. However, at the same time, different levels of technologies for recording and reproducing a digital signal and storing on media for an analog signal give more advantages to a digital representation of the signal, similar to a digital camera versus a film camera.

Lecture 4. Methods of network communication.

Network communication methods

Signals

As mentioned earlier, there are many ways to physically create and transmit a signal, electrical pulses can travel through copper wire, light pulses through glass or plastic fibers, radio signals are transmitted through the air, and laser pulses are transmitted in the infrared or visible range. Conversion of ones and zeros representing data in a computer, into pulses of energy is called coding (modulation).

Similar to the classification of computer networks, signals can be classified based on their various characteristics. Signals are as follows:

analog and digital,

modulated and modulated,

synchronous and asynchronous,

simplex, half-duplex, duplex and multiplex

Analog and digital signals

Depending on the form of electrical voltage (which can be seen on the oscilloscope screen), signals are divided into analog and digital. Most likely, you are already familiar with these terms, as they are quite often found in the documentation of various electronic equipment, such as tape recorders, televisions, telephones, etc. etc.

In a sense, analog equipment represents the outgoing era of electronic technology, and digital equipment is the newest one that is coming to replace it. Keep in mind, however, that one type of signal cannot be better than another. Each of them has its own advantages and disadvantages, as well as its own areas of application. Although digital signals are used more and more widely, they will never replace analog.

Analog signal parameters

Analog signals change smoothly and continuously over time, so they can be graphically represented as a smooth curve (Fig. 4.1).

In nature, the vast majority of processes are fundamentally analog. For example, sound is a change in air pressure that can be converted into electrical voltage using a microphone. Applying this voltage to the oscilloscope input, you can see a graph similar to that shown in Fig. 4.1, i.e. you can trace how the air pressure changes over time.

For a better idea of ​​analog information, think of a traditional in-car speedometer. As the speed of the vehicle increases, the needle moves smoothly on a scale from one number to the next. Another example is tuning to a station in the radio receiver: when you turn the knob, the received frequency changes smoothly.

Most analog signals are cyclical, or periodic, such as radio waves, which are high frequency oscillations of an electromagnetic field. Such cyclic analog signals are usually characterized by three parameters.

Amplitude. The maximum or minimum value of the signal, i.e. wave height.

Frequency. The number of signal cyclic changes per second. Frequency is measured in hertz (Hz); 1 Hz is one cycle per second.

Phase. The position of a wave relative to another wave or relative to a certain point in time serving as a reference point. The phase is usually measured in degrees, and it is believed that the full cycle is 360 degrees.

Digital signal parameters

Another name for digital signals is discrete. Quite often, the term discrete states is encountered. Digital signals change from one discrete state to another almost instantly, without stopping in intermediate states (Fig. 4.2).

An example of a digital signal would be the reading on the latest digital speedometer in a car (compare with the analogue speedometer example in the previous section). When the vehicle speed increases, the numbers showing the speed in kilometers per hour switch in jumps, and the signal value is principally discrete: for example, there are no intermediate values ​​between the discrete states "125 km / h" and "126 km / h". Another example of digital information is a state-of-the-art radio, in which the user enters an exact number equal to the frequency of the radio station to tune in to a specific station.

Digital circuitry is the most important discipline that is studied in all higher and secondary educational institutions that train specialists in electronics. A real radio amateur should also be well versed in this matter. But most of the books and teaching aids written in a language that is very difficult to understand, and it will be difficult for a beginner electronics engineer (possibly a schoolchild) to master new information... A series of new training materials from Master Kit is designed to fill this gap: in our articles, complex concepts are described in the simplest words.

8.1. Analog and digital signals

First you need to figure out how analog circuitry generally differs from digital. And the main difference is in the signals with which these circuits work.
All signals can be divided into two main types: analog and digital.

Analog signals

Analog signals are most familiar to us. We can say that the entire natural world around us is analog. Our sight and hearing, as well as all other sense organs, perceive the incoming information in an analog form, that is, continuously in time. Transmission of sound information - human speech, the sounds of musical instruments, the roar of animals, the sounds of nature, etc. - also carried out in analog form.
To understand this issue even better, let's draw an analog signal (Fig. 1.):

Fig. 1. Analog signal

We see that the analog signal is continuous in time and in amplitude. For any moment in time, you can determine the exact value of the amplitude of the analog signal.

Digital signals

Let's analyze the signal amplitude not constantly, but discretely, at fixed intervals. For example, once a second, or more often: ten times a second. How often we do this is called the sampling rate: once per second - 1 Hz, a thousand times per second - 1000 Hz or 1 kHz.

For clarity, let's draw the graphs of the analog (top) and digital (bottom) signals (Fig. 2.):

Fig. 2. Analog signal (top) and digital copy (bottom)

We see that in each instantaneous period of time it is possible to find out the instantaneous digital value of the signal amplitude. What happens to the signal (according to what law it changes, what is its amplitude) between the "check" intervals, we do not know, this information is lost to us. The less often we check the signal level (the lower the sampling rate), the less information we have about the signal. Of course, the opposite is also true: the higher the sampling rate, the better quality signal presentation. In the limit, increasing the sampling rate to infinity, we get practically the same analog signal.
Does this mean that the analog signal is better than the digital one anyway? In theory, perhaps yes. But in practice, modern analog-to-digital converters (ADCs) operate at such a high sampling rate (up to several million samples per second), so they describe an analog signal in digital form so qualitatively that the human senses (eyes, ears) can no longer feel the difference between original signal and its digital model. A digital signal has a very significant advantage: it is easier to transmit it over wires or radio waves, interference does not significantly affect such a signal. Therefore, all modern mobile connection, television and radio broadcasting - digital.

The lower graph in Fig. 2 can be easily represented in another form - as a long sequence of a pair of numbers: time / amplitude. And numbers are exactly what digital circuits need. Truth, digital circuits prefer to work with numbers in a special way, but we'll talk about that in the next lesson.

Now we can draw important conclusions:

The digital signal is discrete, it can be determined only for certain points in time;
- the higher the sampling rate, the better the accuracy of the digital signal representation.

An analog signal is a data signal in which each of the representing parameters is described by a function of time and a continuous set of possible values.

There are two signal spaces - the space L (continuous signals), and the space l (L is small) - the space of sequences. The space l (L is small) is the space of the Fourier coefficients (a countable set of numbers that define a continuous function on a finite interval of the domain of definition), the space L is the space of continuous signals in the domain of definition. Under certain conditions, the space L is uniquely mapped to the space l (for example, the first two Kotelnikov discretization theorems).

Analog signals are described as continuous functions of time, so an analog signal is sometimes referred to as a continuous signal. Analog signals are opposed to discrete (quantized, digital). Examples of continuous spaces and corresponding physical quantities:

direct: electrical voltage

circumference: the position of the rotor, wheel, gears, analog clock hands, or the phase of the carrier signal

segment: position of the piston, control lever, liquid thermometer or electrical signal, limited in amplitude various multidimensional spaces: color, quadrature modulated signal.

The properties of analog signals are largely the opposite of those of quantized or digital signals.

The lack of clearly distinguishable from each other discrete signal levels leads to the impossibility of applying the concept of information to its description in the form as it is understood in digital technologies. The "amount of information" contained in one sample will be limited only by the dynamic range of the measuring instrument.

No redundancy. From the continuity of the value space, it follows that any interference introduced into the signal is indistinguishable from the signal itself and, therefore, the original amplitude cannot be restored. In fact, filtering is possible, for example, by frequency methods, if any additional information about the properties of this signal is known (in particular, the frequency band).

Application:

Analog signals are often used to represent continuously changing physical quantities. For example, an analog electrical signal taken from a thermocouple carries information about temperature changes, a signal from a microphone - about rapid pressure changes in a sound wave, etc.

2.2 Digital signal

Digital signal is a data signal in which each of the representing parameters is described by a discrete time function and a finite set of possible values.

Signals are discrete electrical or light pulses. With this method, the entire capacity of the communication channel is used to transmit one signal. The digital signal uses the entire bandwidth of the cable. Bandwidth is the difference between the maximum and minimum frequency that can be transmitted over the cable. Each device in such networks sends data in both directions, and some can simultaneously receive and transmit. Baseband systems transmit data as a digital signal of a single frequency.

A discrete digital signal is more difficult to transmit over long distances than an analog signal, therefore it is pre-modulated on the transmitter side, and demodulated on the information receiver side. The use of algorithms for checking and restoring digital information in digital systems can significantly increase the reliability of information transmission.

Comment. It should be borne in mind that a real digital signal is analog by its physical nature. Due to noise and changes in the parameters of transmission lines, it has fluctuations in amplitude, phase / frequency (jitter), polarization. But this analog signal (pulse and discrete) is endowed with the properties of a number. As a result, it becomes possible to use numerical methods for its processing (computer processing).

Very often we hear such definitions as “digital” or “discrete” signal, how is it different from “analog”?

The difference is that the analog signal is continuous in time (blue line), while the digital signal consists of a limited set of coordinates (red dots). If everything is reduced to coordinates, then any segment of an analog signal consists of an infinite number of coordinates.

For a digital signal, the coordinates along the horizontal axis are located at regular intervals, in accordance with the sampling frequency. In the common Audio-CD format, this is 44,100 dots per second. Vertically, the accuracy of the coordinate height corresponds to the digit capacity of the digital signal, for 8 bits it is 256 levels, for 16 bits = 65536 and for 24 bits = 16777216 levels. The higher the bit depth (number of levels), the closer the vertical coordinates to the original wave.

Analogue sources are vinyl and audio tapes. Digital sources are: CD-Audio, DVD-Audio, SA-CD (DSD) and files in WAVE and DSD formats (including derivatives of APE, Flac, Mp3, Ogg, etc.).

Analog Signal Advantages and Disadvantages

The advantage of the analog signal is that it is in the analog form that we perceive sound with our ears. And although our auditory system converts the perceived sound stream into digital form and transfers it in this form to the brain, science and technology have not yet reached the possibility of connecting players and other sound sources directly in this form. Such research is now actively conducted for people with disabilities, and we enjoy exclusively analog sound.

The disadvantage of an analog signal is the ability to store, transmit and replicate the signal. When recording to tape or vinyl, the signal quality will depend on the properties of the tape or vinyl. Over time, the tape will demagnetize and the quality of the recorded signal will deteriorate. Each read gradually destroys the medium, and rewriting introduces additional distortion, where additional deviations are added by the next medium (tape or vinyl), devices for reading, recording and transmitting a signal.

To make a copy of an analog signal is like taking another photograph to copy a photograph.

Advantages and Disadvantages of a Digital Signal

The advantages of a digital signal include accuracy when copying and transmitting an audio stream, where the original is no different from the copy.

The main disadvantage can be considered that the digital signal is an intermediate stage and the accuracy of the final analog signal will depend on how detailed and accurately the coordinates of the sound wave will be described. It is quite logical that the more points there are and the more accurate the coordinates are, the more accurate the wave will be. But there is still no consensus on how many coordinates and data accuracy are sufficient to say that the digital representation of the signal is sufficient to accurately reconstruct the analog signal, indistinguishable from the original by our ears.

In terms of data volumes, the capacity of a conventional analog audio cassette is only about 700-1.1 MB, while a regular CD holds 700 MB. This gives an indication of the need for high-capacity media. And this gives rise to a separate war of compromises with different requirements for the number of describing points and the accuracy of coordinates.

Today it is considered quite sufficient to represent a sound wave with a sampling rate of 44.1 kHz and a bit depth of 16 bits. With a sampling rate of 44.1 kHz, you can recover up to 22 kHz. As psychoacoustic studies show, a further increase in the sampling rate is little noticeable, but an increase in bit depth gives a subjective improvement.

How DACs Build the Wave

A DAC is a digital-to-analog converter, an element that converts digital sound into analog. We will take a quick look at the basic principles. If the comments show interest to consider a number of points in more detail, then a separate material will be released.

Multibit DACs

Very often, the wave is presented in the form of steps, which is due to the architecture of the first generation of multibit R-2R DACs, which operate in a similar way to a switch from a relay.

The DAC input receives the value of the next coordinate along the vertical and in each of its cycles it switches the current (voltage) level to the corresponding level until the next change.

Although it is believed that the human ear hears no more than 20 kHz, and according to Nyquist theory it is possible to restore a signal up to 22 kHz, the question of the quality of this signal after restoration remains. In the high frequency region, the shape of the resulting "step" wave is usually far from the original one. The easiest way out of the situation is to increase the sampling rate when recording, but this leads to a significant and unwanted increase in the file size.

An alternative option is to artificially increase the sampling rate during playback in the DAC by adding intermediate values. Those. we represent the path of a continuous wave (gray dashed line) smoothly connecting the original coordinates (red dots) and add intermediate points on this line (dark purple).

When increasing the sampling rate, it is usually necessary to increase the bit depth so that the coordinates are closer to the approximated wave.

Thanks to intermediate coordinates, it is possible to reduce the "steps" and build the wave closer to the original.

When you see a 44.1 to 192 kHz boost function in a player or external DAC, it’s a function to add intermediate coordinates, not restore or create sound in the region above 20 kHz.

Initially, these were separate SRC microcircuits before the DAC, which then migrated directly to the DAC microcircuits themselves. Today you can find solutions where such a microcircuit is added to modern DACs, this is done in order to provide an alternative to the built-in algorithms in the DAC and sometimes get even better sound (as, for example, it is done in Hidizs AP100).

The main refusal in the industry from multi-bit DACs occurred due to the impossibility of further technological development of quality indicators with current production technologies and a higher cost versus "pulse" DACs with comparable characteristics. Nevertheless, in Hi-End products, preference is often given to old multi-bit DACs, rather than new solutions with technically better characteristics.

Pulse DAC

In the late 70s, an alternative version of DACs based on a "pulse" architecture - "delta-sigma", became widespread. Pulse DAC technology made possible the emergence of ultra-fast switches and allowed the use of a high carrier frequency.

The signal amplitude is the average value of the pulse amplitudes (pulses of equal amplitude are shown in green, and the final sound wave is shown in white).

For example, a sequence of eight clock cycles of five pulses will give an average amplitude (1 + 1 + 1 + 0 + 0 + 1 + 1 + 0) / 8 = 0.625. The higher the carrier frequency, the more pulses will be smoothed and the more accurate the amplitude will be. This made it possible to present the audio stream in one-bit form with a wide dynamic range.

Averaging can be done with an ordinary analog filter, and if such a set of pulses is applied directly to the speaker, then we will get sound at the output, and ultra high frequencies will not be reproduced due to the large inertia of the emitter. PWM amplifiers in class D work according to this principle, where the energy density of the pulses is created not by their number, but by the duration of each pulse (which is easier to implement, but cannot be described with a simple binary code).

A multi-bit DAC can be thought of as a printer capable of applying color with pantone inks. Delta-Sigma is an inkjet printer with a limited set of colors, but due to the ability to apply very small dots (in comparison with an antler printer), due to the different density of dots per unit surface, it gives more shades.

In the image, we usually do not see individual points due to the low resolution of the eye, but only the middle tone. Likewise, the ear does not hear the impulses separately.

Ultimately, with current technologies in pulse DACs, you can get a wave close to the one that theoretically should be obtained when approximating intermediate coordinates.

It should be noted that after the appearance of the delta-sigma DAC, the urgency to draw a "digital wave" with steps has disappeared, since so modern DACs do not build a wave with steps. Correctly construct a discrete signal with points connected by a smooth line.

Are switching DACs ideal?

But in practice, not everything is cloudless, and there are a number of problems and limitations.

Because the overwhelming number of records are stored in a multi-bit signal, then conversion into a pulse signal according to the “bit-for-bit” principle requires an unnecessarily high carrier frequency, which modern DACs do not support.

The main function of modern pulse DACs is to convert a multi-bit signal into a one-bit one with a relatively low carrier frequency with data decimation. Basically, it is these algorithms that determine the final sound quality of impulse DACs.

To reduce the problem of a high carrier frequency, the audio stream is split into several one-bit streams, where each stream is responsible for its own group of discharge, which is equivalent to a multiple increase in the carrier frequency of the number of streams. These DACs are called multi-bit delta-sigma DACs.

Today, pulse DACs have received a second wind in high-speed general-purpose chips in NAD and Chord products due to the ability to flexibly program conversion algorithms.

DSD format

After the widespread use of delta-sigma DACs, it was quite logical that the binary code format appeared directly in delta-sigma encoding. This format is called DSD (Direct Stream Digital).

The format was not widely used for several reasons. Editing files in this format turned out to be unnecessarily limited: you cannot mix streams, adjust the volume and apply equalization. This means that without loss of quality, you can only archive analog recordings and make a two-microphone recording of live performances without further processing. In a word, you can't really make money.

In the fight against piracy, SA-CDs were not supported (and are not supported until now) by computers, which prevents them from making copies. No copies - no general audience. It was possible to play DSD audio content only from a separate SA-CD player from a branded disc. If for the PCM format there is an SPDIF standard for digital transmission of data from a source to a separate DAC, then there is no standard for the DSD format and the first pirated copies of SA-CD discs were digitized from the analog outputs of SA-CD players (although the situation seems silly, but in reality some recordings were released only on SA-CD, or the same recording on Audio-CD was specially made poorly to promote SA-CD).

The turning point occurred with the release of the SONY game consoles, where the SA-CD disc was automatically copied to the console's hard drive before being played. Fans of the DSD format took advantage of this. The advent of pirated recordings stimulated the market to release separate DACs for playing DSD streams. Most external DACs with DSD support today support USB data transfer using the DoP format as a separate digital signal encoding over SPDIF.

The carrier frequencies for DSD are relatively small, 2.8 and 5.6 MHz, but this audio stream does not require any decimation conversions and is quite competitive with high-definition formats such as DVD-Audio.

There is no definite answer to the question of which is better, DSP or PCM. Everything rests on the quality of the implementation of a specific DAC and the talent of the sound engineer when recording the final file.

General conclusion

Analog sound is what we hear and perceive as the world around us with our eyes. Digital sound is a set of coordinates that describe a sound wave, and which we cannot directly hear without converting it into an analog signal.

An analog signal recorded directly onto an audio tape or vinyl cannot be re-recorded without loss of quality, while a wave in digital form can be copied bit by bit.

Digital recording formats are a constant trade-off between the amount of coordinate accuracy versus file size, and any digital signal is only an approximation to the original analog signal. However, at the same time, different levels of technologies for recording and reproducing a digital signal and storing on media for an analog signal give more advantages to a digital representation of the signal, similar to a digital camera versus a film camera.