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Fundamentals of digital audio

Digital audio is based on the mathematical representation of the sound wave.

The digital world is evolving very rapidly and it is no wonder that many people find digital technology complex. The purpose of this article is to explain what digital audio is without going into complicated mathematical details. To understand what digital sound is, you must first understand that there are no sounds inside a computer and there is only one math.

What is sound
Sound is the vibration of molecules. Mathematically, sound can be accurately described as a “wave.” It has a maximum peak value (wave hump) and a minimum value (deflection). If you have ever seen a graphical representation of a sound wave, you will notice that sound is always represented by a curve that constantly crosses the X-axis. This means that the nature of sound is “periodic”. Any sound has a crest and deflection, a positive and a negative period. This is called a loop. So the basic concept is that all sounds have at least one cycle.

The next important idea is that any periodic function can be represented mathematically as a series of sinusoids. In other words, even the most complex sound is just a collection of sine waves. A voice can constantly change its volume and pitch, but anytime it sounds, the voice is just a set of sine waves.

And finally, third: people do not hear sounds with a frequency higher than 22 kHz. Therefore, it is not necessary to record everything above 22 kHz.

So once again, the fundamentals of sound are as follows:

Sound waves are periodic and therefore can be described as a collection of sine waves.
We are not interested in waves with a frequency higher than 22 kHz, because we cannot physically hear them.
Analog to digital transition
Let’s say I’m speaking into a microphone. The microphone turns my voice into a continuous electrical current. This electrical current passes through a wire through an amplifier of some kind and eventually enters an analog-digital converter (ADC). Remember that the computer does not store sounds, but mathematical values, so we need something that converts the analog stream into a sequence of ones and zeros. This is what the ADC is doing. In simple terms, the converter takes quick snapshots of the sound wave, called samples, and assigns an amplitude value to each sample. And here we come to two basic concepts that will help explain the nature of digital sound. These concepts are time and breadth.

Sound bitness
Sound bitness
In the digital world, nothing is continuous, everything has a certain mathematical meaning. In the analog world, the sound wave will reach its peak and all values ​​from 0 dB to the peak will exist. And in a digital signal, there are a limited number of possible amplitude values. Think of analog audio as someone who gently walks up an escalator, while digital audio is someone who walks up a staircase and, over time, is on one rung or the other. Or let’s say there are values ​​50 and 51. So in analog sound there may be some intermediate value of 50.46, but in digital sound this value will be rounded to 50. This means that in fact the sound wave is distorted as it passes through the ADC … And since the analog signal is continuous, then this rounding of values ​​occurs constantly during the conversion process. This is called a quantization error and it sounds like a strange noise. But imagine a ladder with more steps that are less high. Now we have the values ​​50, followed by 50.2, followed by 50.4, and then 50.6, etc. An analog signal with an amplitude value of 50.46 will now be rounded to 50.4 instead of 50. This is a major improvement that does not completely eliminate quantization errors, but significantly reduces their impact. An increase in bitness is essentially an increase in the number of steps on a stair with a decrease in their height. As the quantization error decreases, the noise level decreases. Now we have the values ​​50, followed by 50.2, followed by 50.4, and then 50.6, etc. An analog signal with an amplitude value of 50.46 will now be rounded to 50.4 instead of 50. This is a major improvement that does not completely eliminate quantization errors, but significantly reduces their impact. An increase in bitness is essentially an increase in the number of steps on a stair with a decrease in their height. As the quantization error decreases, the noise level decreases.

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What is digital audio

Digital audio is a numerical representation of sound.

Recording sound as digital sound is similar to recording sound on a tape recorder. Let’s say you have a microphone connected to your computer. Whenever a sound is heard (speaking, singing, playing a musical instrument or just any noise), the microphone “hears” it and converts the sound into an electrical signal. The microphone then sends the signal to the computer’s sound card, which converts the signal into numbers. These numbers are called samples.

A sound card is a device that is inserted into a computer that allows it to understand the electrical signals from any sound device. You can think of a sound card as a “translator”. When an audio device (such as a microphone, electronic musical instrument, CD player, or other device capable of outputting an audio signal) sends signals to the computer, the sound card receives the signals and converts them into numbers that computer can understand.

The samples contain information that tells the computer what the recorded signal sounded like at specific times. The more samples that are used to represent the signal, the higher the quality of the recorded signal. For example, to create a digital sound recording that has the same quality as a CD recording, the computer must receive 44,100 samples per second. The number of samples taken per second is called the sample rate.

The size of each individual sample also affects the quality of the recorded sound. This size is called the bit depth. The higher the bit depth, the higher the sound quality. For example, to create CD-quality digital audio, each sample must be 16-bit.

Computers use the binary form to represent numbers. The place of a binary number is called a bit, each bit represents one of two numbers: 1 or 0. By combining bits, computers can display any number. For example, any number between 0 and 255 is represented as an eight-bit number. With 16 bits, it can represent numbers in the range 0 to 65,535.

Your computer can save all submitted samples. The temporal characteristics of the sample are also saved. Later, the computer can send samples to the sound card at the same intervals, so you hear the sound exactly the same as what was recorded. The basic concept is as follows: a sound card records an electrical signal from an audio device (such as a microphone or a CD player). The sound card converts the signals into sets of numbers, called samples, that are stored on your computer. During playback, the samples are sent back to the sound card, which converts them into an electrical signal. The signal is sent to the speakers (or other audio device) and you hear the sound exactly as you recorded it.

So what is the difference?
After reading the description of MIDI and digital audio, you may still be confused about the difference between the two. After all, both processes record the signals sent to the computer and then reproduce them, right? The point is, when you record MIDI data, you are not recording actual sound. Just record the instructions for playback. It is like a musician playing notes, where the notes are MIDI data and the musician is the computer. The musician (or computer) reads the notes (or MIDI data) and then stores them in memory. The musician then plays a melody on a musical instrument. What if the musician takes another instrument to play? The game will remain the same, but the sound will change. The same is true for MIDI data.

A keyboard synthesizer can produce any sound, but playing the same MIDI data using the keyboard will be exactly the same.

When you record digital audio, you are recording real audio. If you record a performance of a piece of music as digital sound, you cannot change the sound of that performance as described above. Due to these differences, MIDI and digital sound have their own advantages and disadvantages. Since MIDI is recorded as data for playback, rather than actual sound, you have much more freedom to manipulate the sound than with digital sound. For example, you can easily correct the error by changing the pitch. MIDI data can be converted to standard music notation, which is not possible with digital sound.

The benefits of digital audio

The basics of “numbers”

Each of the multimedia devices on sale today, be it a CD player, a voice recorder or a flash memory player, uses many different types of presentation of data streams, which are then converted into sound. And even more sound formats used for professional purposes have been invented. An inexperienced buyer is forced to gather information on designations on boxes and devices from a variety of sources, often receiving incorrect information or even more confusion.

Almost all devices in the “Portable Audio” section of the ZOOM.CNews.ru catalog support multiple sound formats at the same time, and many devices that do not belong in this category are also tagged with support for playing sound files. To help our reader, we decided to create a short glossary of abbreviations and talk about the most common formats. We plan to leave it open for updates and modifications, adding new formats and describing in more detail the advantages and disadvantages of the already common or forgotten ones.

A little theory

To begin with, remember that digital sound is nothing more than a collection of numbers. The determining factor is the system by which sound as air pressure is converted into data streams and encoded for further processing and reproduction. Consequently, digital sound is usually included in computer files with various extensions, which more often (but not always) can determine their format. And the same concept of format can have, paradoxically, two meanings. First, the format may exist as a general characteristic, including both the type and the physical characteristics of the medium (disc or cassette), method of recording, principles of encoding, and protection against errors. Second, the format can only be understood as the method of encoding and compressing sound, as standard means are used for transfer, for example a computer.

Analog sound, unlike digital, is reproduced on analog devices and has several significant differences. While not a data stream, analog sound is represented as a continuous electrical signal that represents the change in sound wave. To translate it into digital format, the sound is “digitized”, that is, it is divided into certain segments, in which the numerical value of the amplitude is fixed at that moment. We will not delve into the principles of digital sound creation, but it is absolutely necessary to note that the more often a sound segment is divided and its characteristics described, the clearer and more complete the sound image itself is created.

This process generates an enormous flow of data that describes the sound, and it is clear that each digital audio format is nothing more than a compromise between the need to present the sound as loud as possible and the limitations of the memory of the computer or device. Of reproduction.

A little more theory. In most cases, the human ear perceives sound with a frequency no higher than 22,000 Hz and, to describe it fully in digital form, a sampling frequency of at least 44.1 kHz is required. Since it is absolutely impossible to determine the value of the signal at any given time, during digitization quantization occurs, that is, the replacement of the actual values ​​of the signal by approximate values. The more levels of audio quantization, the more accurately the signal level is described. As a result, each standard CD carries an audio signal with a sampling frequency of the same 44.1 kHz and a 16-bit quantization level,

Is the digital signal distorted during transmission and storage?

Since any digital signal is represented as a real voltage or current electrical curve, its shape is distorted in one way or another during any transmission, and a signal “frozen” for storage (signalogram) is subject to degradation due to physical reasons. common.

All of these influences on the shape of the carrier signal are interferences that, up to a certain value, do not change the information content of the signal, since individual distortions and letter loss in words generally do not interfere with the correct understanding of words. words, and information redundancy, such as an increase in the length of the words, increases the probability of successful recognition. … In other words, the carrier signal itself can be distorted, but the information it carries, the encoded audio signal, remains unchanged in the vast majority of cases.

So that the quality of the carrier signal does not deteriorate, any transmission of useful audio information (copying, writing to a carrier and reading it) must necessarily include the operation of restoring the form of the carrier signal, and ideally, and the digital form primary of the information signal, and only after that the newly generated carrier signal can be transmitted to the next consumer. In the case of direct copy without restoration (for example, simply rewriting a video cassette with a digital signal obtained with a PCM decoder in common VCRs), the quality of the digital signal deteriorates, although it still contains all the information it carries. However, after repeated sequential copies or long-term storage, the quality deteriorates so much that unrecoverable errors begin to appear that irreversibly distort the information carried by the signal. Therefore, the copying and transmission of digital signals should be done only on digital devices and, when stored on media, should be “updated” in a timely manner without waiting for irreversible degradation (for magnetic media, this period is estimated to be several years ). A correctly transmitted or updated digital signallogram does not lose quality and can be copied and exist forever in absolutely unaltered form. without waiting for irreversible degradation (for magnetic carriers this period is estimated to be several years). A correctly transmitted or updated digital signallogram does not lose quality and can be copied and exist forever in absolutely unaltered form. without waiting for irreversible degradation (for magnetic carriers this period is estimated to be several years). A correctly transmitted or updated digital signallogram does not lose quality and can be copied and exist forever in absolutely unaltered form.

However, it should not be forgotten that the correctness of any code is finite, and the actual carriers are far from ideal, therefore the occurrence of unrecoverable errors is such a rare thing, especially with careless handling of the carrier. When reading new and correctly stored DAT cassettes or CDs on high-quality and reliable devices, these errors practically do not occur, however, with aging, contamination and damage of media and reading systems, they become more. A single uncorrected error is almost always invisible to the ear due to interpolation, however, it leads to distortion of the original sound signal, and the accumulation of such errors over time begins to be felt in the ear.

A separate problem is the difficulty of recording uncorrected errors, as well as verifying the identity of the original and the copy. Very often, designers of digital audio devices operating in real time do not care about the issue of accurate verification of the reliability of the transmission, considering that the measures taken to correct the errors are sufficient. In the general case, the impossibility of retransmitting an erroneous sample or block leads to interpolation occurring secretly and after copying it is impossible to say with certainty whether the original signal was copied exactly. Error indicators, which are found on some devices, usually light up only at the moment of their appearance, and in the case of single errors, their operation can easily go unnoticed. Even in personal computer-based systems, it is often impossible to control the accuracy of reception through a digital interface or direct reading from a CD; the only way out is to repeat the operation and compare the results.

What are the pros and cons of digital audio?

The digital representation of sound is valuable, first of all, for the possibility of endless storage and reproduction without loss of quality; however, the conversion from analog to digital and vice versa inevitably leads to its partial loss.

The most unpleasant distortions introduced in the digitizing stage are the granular noise that occurs when the signal is quantized by level due to rounding of the amplitude to the nearest discrete value. Unlike simple broadband noise introduced by quantization errors, granular noise is the harmonic distortion of the signal, most noticeable in the upper part of the spectrum.

The power of the granular noise is inversely proportional to the number of quantization steps; However, due to the logarithmic characteristic of hearing with linear quantization (constant step value), quiet sounds have fewer quantization steps than loud sounds, and as a result, the main density of non-linear distortions falls in the region of sounds. silent. This leads to a limitation of the dynamic range, which ideally (without taking into account harmonic distortion) would be equal to the signal-to-noise ratio, but the need to limit this distortion reduces the dynamic range for 16-bit encoding to 50-60 dB. The situation could have been saved by logarithmic quantification, but its implementation in real time is very difficult and expensive.

The distortion introduced by granular noise can be reduced by adding normal white noise (random or pseudo-random signal) to the signal, with an amplitude of half the least significant bit; such an operation is called dithering. This leads to a slight increase in the noise level, but weakens the correlation of quantization errors with the components of the high-frequency signal and improves subjective perception. Anti-aliasing is also applied before rounding the samples by decreasing their bit depth. Essentially, dithering and noise shaping are special cases of the same technology, with the difference that, in the first case, white noise with a flat spectrum is used and, in the second, noise with a spectrum with a “shape “special.

When restoring audio from digital to analog, there is the problem of smoothing the stepped waveform and suppressing the harmonics introduced by the sample rate. Due to the imperfection of the frequency response of the filters, insufficient suppression of this interference or excessive attenuation of useful high-frequency components may occur. Poorly suppressed sample rate harmonics distort the shape of the analog signal (especially in the high frequency region), resulting in a “rough” and “dirty” sound.