Why upsampling? Part 1

When it comes to improving digital sound quality, experts in this field agree on only one thing: As the sample rate increases, the sound quality improves dramatically.

Also, under the word “improve”, everyone already understands something of their own. All the variety of opinions on this topic boils down to the following: the sound becomes clearer, softer, more natural, the low frequencies are perceived more clearly.

However, these nuances are only noticed by listeners trained with a good ear for music on specially selected sound material and using technically advanced equipment.

There are many hypotheses that explain why sound quality is improved by sampling. Many technicians are inclined to believe that this relationship is due to distortions that arise from filtering and interpolation during reconstruction of the audio signal.

On a modern technical level, high-quality interpolators may be practically impossible to implement, therefore instead of improving them, manufacturers simply increase the sampling rate. Maybe it’s not about them at all.

Another version, which many music lovers adhere to, is that at a low sampling frequency, for example 44100 Hz, digital sound is completely devoid of nuances of high sounds, the main frequencies of which are above 7 kHz. , and at lower frequencies there are too few nuances for high quality. perception of music.

In fact, many musical instruments generate vibrations of up to 100 kHz. It is true that the proportion of energy that falls in the frequency band above 20 kHz is 0.01 to 2% for sounds of a harmonic nature and 0.02 to 68% for sounds created by a cymbal, triangle or hitting a drum rim. metal (hoop shot – Editor’s note).

Even the frequency range of speech in hissing-hissing sounds extends up to 40 kHz. Supporters of this version are not ashamed that a person cannot perceive sounds with a frequency higher than 20 kHz. Ultrasound is assumed to be perceived bypassing the auditory system, for example, through bone conduction.

Rumors that harmonics above 20 kHz contribute significantly to sounding have led to the creation and widespread introduction of analog-to-digital converters using 96 kHz and 192 kHz sample rates; The sampling frequency is expected to increase to 384 kHz.

Based on modern knowledge of human perception of sound, it must be assumed that the relationship between digital sound quality and sampling frequency is due to the transformation of the quantization error spectrum in the audio frequency range.

In the technical literature, this topic is considered only for a particular mathematical model, when music is represented by a signal with a uniform distribution in level and frequency. In this case, the quantization errors are converted to noise with a uniform spectral density from 0 Hz to the Nyquist frequency.

For every doubling of the sampling frequency, the spectral noise density is reduced by half and the signal-to-noise ratio increases by 3 dB. Since the pressure resolution limit is approximately 1 dB, these decibels are unlikely to have a noticeable effect on sound perception in the high-frequency region. Based on these numbers, it is absolutely impossible to draw tentative conclusions about the change in sound quality.

In order to relate the spectrum of quantization errors, sampling frequency and sound quality, in this article it is proposed to use a tonal signal as a music model, as is usual to evaluate the quality of sound paths. This approach is largely based on materials published in the “Sound Engineer” magazine.

The results can be summarized as follows. Unlike analog audio, digital audio is the product of amplitude modulation. This is manifested in a rigid functional dependence of the frequency multiplicity factor quantization error spectrum of the audio signal frequency F and the sampling frequency fs, represented as the ratio of the prime numbers y and x (k = fs / F = y / x). The frequency spectrum of quantization errors is always discrete and is uniquely determined by the multiplicity factor; the components of this spectrum are also uniquely determined by the amplitude of the audio signal, expressed in quanta. This means that the mechanism for the formation of the quantization error spectrum does not depend on the number of bits used. With an increase in quantization bit depth.