# Secret of high quality sound. 44.1 and 192 kHz. Part 1

From the moment occurrence digital formats of home sound, announced unsurpassed cleanliness of sound, full absence of "vinylic" cracklings and noise in pauses, have started to inflame serious discussions on "dryness" of CD-sound and absence of "softness" vinyl. Was burned whole galaxy of sound processing effects (plug-ins), imposing noise and cracklings of vinil on qualitative CD-record. But from it sound of CD all the same did not become neither it is better, nor is worse, but only, similarly to an electric fireplace with an artificial flame, - is slightly cosier.

So why the morally-become outdated vinyl frequently experts admits, a better source of a sound, than CD? Whether there is no in it what shamanism? We shall try to reject mysticism and to understand with cleanly technical side of a question.

## 44.1 and 192 kHz

What there is a sound? Physically is air pressure, changing during time, upon an eardrum of a human ear . Force of pressure repeats the form of an input electric voltage of acoustic systems. Any form of voltage can be presented, as the sum of infinite amount of sinusoids with various:

- Amplitudes (roughly speaking, force of fluctuation);

- Frequencies (amount of cycles [the periods, repetitions] sinusoids in second or Hertz [Hz]) from 0 to infinity;

- Phases (it is rough: a relative time delay between this sinusoids).

Experimentally was accepted (I shall notice: for an average ear), that the person hears frequencies from 20 up to 20000 Hz. We shall try to bind these numbers to keys of the piano. The uppermost note of a piano (ля 4-th octaves) has frequency of 3520 Hz (3520 cycles in a second). The sound of a piano consists not only of one this sinusoid (1-st harmonic), but also from sinusoids: 3520 Hz * 2=7040 Hz (2-nd harmonic); 3520 Hz * 3=10560 Hz (3-rd harmonic); …; 3520 Hz * 5=17600 Hz (5-th harmonic).

Conversion of these sinusoids (uninterrupted in time) to digital signal: Analog-digital converter (ADC) will transform a sound (for example, signal on an input of sound card) to the digital samples representing value of signal's level by regular time intervals.

If sampling rate is equal 44.1 kHz (kilohertz) it means, that every second is measured on 44100 values of signal's levels (samples).

The **initial signal** (as well as a signal on a vinyl) changes smoothly without jumps. Signal restored from digital samples - already represents "square" (step) line as a signal level at output of the digital-analog converter (DAC) keeps to constants until time of the next readout will come.

The first harmonic of the top note of a piano has 3520 cycles in a second. For one cycle has time to make 12 samples. That is, instead of uninterrupted function, we see 12 steps. And the fifth harmonic (17600 cycles in a second) already represents only 2 steps.

Tell to me now: whether sinusoids and rectangulars are very similar to hearing? The musicians working with synthesizers, will understand me. In analog synthesizers there are generators of sine wave, rectangular, triangular and other forms of wave. Even the unsophisticated hearing will notice distinction between rectangular and sine wave. Approximately too most occurs at comparison of a continuous initial analog signal to its restored step image. And, distortions are aggravated with growth of frequency of a signal (number of a harmonic). It is "dryness" of CD digital record.

The people familiar with Nyquist theorem, know, that at analog-digital conversion signal, sampling frequency (amount of measurements for a second) should exceed the maximal frequency of a signal (i.e. the top heard frequency 20 kHz) in 2 times that 40 kHz makes. But for what it is enough? Nyquist theorem was developed for infinite signals. It mean, not for un-periodical continuously varying wave form of audio records.

Now we shall return to the fifth harmonic of the top note of a piano which in the wonderful image has turned from a sinusoid to a rectangular. With growth of frequency of digitization up to 192 kHz - it will consist any more from 2, and of the whole 11 steps, that, all the same, will remind more initial analog signal.