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Basics of digital sound theory Part 3

Compression algorithms

Let’s try to calculate how much disk space an average CD-quality digitized music composition will occupy. Obviously, for this it is necessary to use the formula t KBF size ⋅ ⋅ ⋅ = where F is the sampling frequency, B is the sample capacity, K is the number of strings, t is the time.

Assuming 44.1 kHz herbal, B = 2 bytes, K = 2 channels, and t = 300 seconds, we get that the digitized song will occupy approximately 50MB.

This means that only about 10 uncompressed songs can be burned to CD. Since every second of digitized CD quality sound takes up almost 200 Kb, this sound will be very problematic to use on telephony, radio or the Internet. Even if you digitize the sound as a single channel with a sample rate of 11.05 kHz and a bit depth of 8 bits, each second will occupy 11 KB.

For ordinary telephone networks, this is too much for sound to be transmitted in a continuous stream. A problem arises: somehow it is necessary to reduce the size of the sound files.

It is solved quite effectively by using various compression algorithms.
Flash Player supports the following types of compression.

• ADPCM (Adaptive Differential Pulse Code Modulation – Adaptive Difference Pulse Code Modulation). This type of compression is based on two ideas. First, it was found that in the vast majority of sounds we perceive, slowly changing low-frequency components prevail. From this fact it follows that the difference between adjacent samples is often small (or rather, significantly less than the absolute value of the samples themselves).

This means that the digitized audio signal can be represented not by the samples themselves, but by the differences between them, which are smaller in magnitude and therefore require fewer bits for description. Second, the coding of the difference between adjacent samples is done taking into account the magnitude of the amplitude and frequency composition, since the human ear has sensitivity limits (the so-called adaptation).

The ADPCM algorithm is actively used in IP telephony. It is poorly suited for streaming music due to the significant distortions it introduces into sound (distortions, of course, get into speech, but are hardly noticeable in speech). The compression ratio for ADPCM is typically low, ranging from 8: 1 to 3: 1. The ADPCM Flash Player codec allows 2, 3.4, or 5 bits to represent the difference between samples. Actually, you can achieve acceptable sound quality with a bit rate (bit rate, that is, the “weight” of a second of sound) of 16 Kbit.

The ADPCM algorithm is significantly inferior to MP3, so it is not worth using such compression in principle. MP3 compression will provide an order of magnitude better quality with the same bit depth. The presence of the corresponding codec is explained by the principles of backward compatibility: the MP3 codec is built into the player only in Flash 4. Before that, only the ADPCM codec was used, which is probably due to the free distribution of this algorithm. The reason ADPCM is still used in IP telephony is that it does not require as extensive math calculations as MP3, so compression can be done on the fly.

• MP3. One of the first and most common compression algorithms based on the so-called psychoacoustic compression. It uses the following characteristics of the human ear:

or if a soft sound follows a very strong one, then we don’t hear it. Therefore, it can be discarded;

or a sound component with a large amplitude masks components close to it in frequency, but with smaller amplitudes. Therefore, they can be slaughtered without noticeable loss of quality;

or the ear’s sensitivity to frequency distortion is low, therefore, if the components are close, they can be considered the same;

o We misperceive very low and very loud sounds, so fewer bits can be allocated for their encoding than for sounds with an average frequency.

Technically, the MP3 algorithm is implemented as follows. The sound is divided into chunks of a certain length called frames, and a forward Fourier transform is applied to each set of samples. Its result is the decomposition of a sound wave into elementary sinusoids of different frequencies: harmonics. The harmonic coefficient determines its contribution to the resulting wave. Harmonic coefficients are compared and the least significant are discarded.

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Basics of Digital Sound Theory Part 2

A sample rate of 44.1 kHz is not always ideal.

When transmitting data over a low-bandwidth network, the quality of the sound must be sacrificed in favor of its size, in practice sampling frequencies two, four and eight times lower than 44.1 kHz are usually used:

• 22.05 kHz: the so-called radio quality. Used when encoding the sound of FM radio stations. In the case of Flash, it is good for creating background music and event sounds. For the transmission of a human voice, it is even somewhat redundant;

• 11.025 kHz – telephone quality. A sample rate more suitable for the human voice. Used in 1P telephony;

• 5.5 kHz: sound about to lose the information component. This sample rate can be used to transmit low sounds as well as speech (albeit with mediocre quality).

Flash Player supports sample rates 44.1: 22.05; 11,025; 5.5 kHz. The choice of frequency should be determined by the type of sound, as well as the importance of maintaining the size of the SWF file. However, it should be remembered that there is no point in increasing the sample rate of the audio fragment compared to the initial one. This will not increase the quality, but will only unnecessarily increase the size of the movie.

Bit depth of samples
Bit depth determines how many different amplitude values ​​can be captured during digitizing. If the bit width is 4 bits, then the range of the amplitude value from zero to the maximum will be divided into only 16 bins. Naturally, the error when rebuilding the analog signal will be very high. This bit depth is suitable for representing very simple sounds as well as speech (its quality will be low).

The 8-bit width allows 256 amplitude values ​​to be represented. This is the bit depth used by FM radio stations. It is enough to present any sound in satisfactory quality. 16-bit encoding is optimal. At the same time, it can work with 65,536 amplitude options, which is enough to cover the entire audible range.

The 16-bit format is used for CD recording. Higher quality quantization is only justified in the case of studio sound processing.

Flash Player supports 8-bit and 16-bit quantization for uncompressed formats (for example, WAV) and only 16-bit for compressed formats (MP3 belongs to them). Keep this in mind when importing a sound file into a movie.

Number of channels The
Stereo sound is designed to give the playback sound a natural dimension. This is achieved due to the fact that a different component of sound is reproduced from each speaker. In general, the sound of each channel is a separate sound file, so the size of the stereo sound is proportional to the number of channels supported.

Conventional non-professional sound cards work with two-channel audio. The Flash player also supports the same number of channels. With ActionScript, you can mix the sound of the channels by playing the left channel on the right speaker and the right channel on the left. How this is done, we will talk a bit below.

If the sound is encoded in MP3 format, you can choose one of three stereo formats.

• Dual channel. Each channel receives half of the stream and is separately encoded as mono. It is mainly recommended in cases where different channels contain a fundamentally different signal, for example text in different languages.

• Stereo. The channels are scrambled separately, but the scrambler program can give one channel more space than the other if necessary. Most standard format.

• Joint stereo. The stereo signal is divided into two new channels. One is the average of the original channels and the other is the difference between the channels. In this mode, the sound quality is obtained more frequently than in others.

Unfortunately, in the Flash development environment, you cannot specify which stereo format is used. Therefore, if sound quality is of paramount importance, then the creation of MP3 files with the required parameters should be done using one of the specialized programs.

Basic concepts of digital sound theory

Sound is, in general, the vibrations of an elastic medium.

The sound is caused by mechanical vibrations of some object (this can be a string, vocal cords, etc.) in contact with the environment. The frequency of vibration (measured in Hertz) determines the pitch. The higher the frequency, the louder the sound. The human ear can perceive sound vibrations from the air with a frequency of 20 Hz to 20 kHz. The ear perceives the amplitude of the vibration as volume. The higher the amplitude, the louder the sound.

Electromagnetic waves are a direct analog of sound waves. The latter are less susceptible to dispersal by the environment, the information they carry is easier to store and process. Electromagnetic waves are the most important secondary carrier of sound. The transformation of acoustic waves into electromagnetic waves (as well as the reverse operation) is carried out due to the usual induction effect, which consists in the appearance of a current in a conductor when it is placed in an alternating magnetic field.

Simply put, the oscillation of the loudspeaker membrane magnet near the coil induces an alternating current in it. If this current is applied to another speaker, then the magnet on its membrane will move, creating a corresponding sound.

This is how the telephone and the radio work.

Sound converted to electromagnetic waves can be easily stored. For this, some parameter of the carrier must be compared (the depth of the plate track or the degree of magnetization of the film) with the amplitude of the oscillations (that is, the strength of the induced current in the speaker coil) . Sound converted directly to electromagnetic waves is called analog sound. Its main characteristic is the direct correspondence of the electromagnetic waves transmitted or recorded with the acoustic ones.

Digital sound is relatively new. Its main difference from analog is discretion. When digitizing, a special device, an analog-to-digital converter (ADC), measures at regular intervals (approximately 0.001-0.0001 seconds) the magnitude of the amplitude of an electromagnetic wave corresponding to an analog sound form and writes its value to a file with a specified precision. This value is generally called sample, or in jargon, sample (of the sample in English, sample). The same digitization is often called sampling or sampling.

By converting sound from digital to analog (this is done by a device called a digital-to-analog converter (DAC)).

The interpolation (approximation) of the intermediate values ​​of the amplitude is carried out according to the known ones. Since the sampling frequency is usually high, this operation allows you to fairly accurately reconstruct the original analog signal.

The digital form of sound is characterized by five parameters.

1. The sampling rate;
2. Bit size of the samples.
3. The number of channels or tracks.
4. Compression / decompression algorithm (codec).
5. Storage format.

Since each of these parameters is quite specific, we will consider them separately.

Sampling rate
The sample rate determines how many samples per second will be taken when digitizing. If we compare digital sound with digital images, then the sample rate will correspond to the resolution (a more “realistic” analogy is the frame rate in cinema). The higher the sampling frequency, the better it is possible to reconstruct the analog signal based on the digital form of the sound (more precisely, the higher the sampling frequency, the broader the spectrum of frequencies that can be recorded during digitization).
The famous Nyquist-Kotelnikov theorem states that for the correct reconstruction of an analog signal from its digital recording, it is necessary that the sampling frequency be at least twice the maximum sound frequency.

Since the upper listening limit is 20 kHz, ideally the sample rate should be at least 40 kHz. This is why the standard sampling frequency used for recording CDs is 44.1 kHz (so-called CD quality). However, the sample rate can be higher, but this sound quality is only used by recording studios and especially demanding music lovers.