Bits, Hertz, Shaped Dithering … Part 3
What is behind these concepts?
For transmission of sound as is, it would be nice to keep the entire perceived range from 10 Hz to 20 kHz. In theory, there is absolutely no problem with low frequencies in digital recording (but there are problems with transmitting these frequencies through electrical circuits and reproducing them through small stereo speakers or headphones). So, at the output of the sound cards there is usually a power amplifier, which feeds the signal to the stereo speakers. This inexpensive board amplifier, together with the feedback circuit, as well as the parasitic capacitances, forms a low pass filter that “dumps the bass.”
With high frequencies, things are a bit worse, at least definitely more complicated. Most of the essence of the DAC and ADC enhancements and complications is aimed precisely at more reliable transmission of high frequencies. “High” means frequencies comparable to the sampling frequency, that is, in the case of 44.1 kHz, it is 7 to 10 kHz and more.
Imagine a 14 kHz sinusoidal signal digitized at a 44.1 kHz sample rate. There are about three points (samples) for one period of the input sinusoid, and to restore the original frequency as a sinusoid, you need to show some imagination. The sample waveform restoration process also occurs in the DAC, this is done using the restoration filter. And if the relatively low frequencies are almost pre-cast sinusoids, then the shape and consequently the quality of the reconstruction of the high frequencies is completely dependent on the conscience of the DAC restoration system. Therefore, the closer the signal frequency is to one-half the sampling frequency, the more difficult it is to reconstruct the shape of the signal.
This is the main problem when it comes to reproducing high frequencies. However, the problem is not as serious as it might seem. All modern DACs use resampling (multi-rate) technology, which involves restoring digitally to a sample rate several times higher and then converting it to an analog signal at an increased rate. Thus, the problem of restoring high frequencies shifts to the shoulders of digital filters, which can be of very high quality. So high quality that in the case of expensive devices the problem is completely eliminated: distortion-free reproduction of frequencies up to 19-20 kHz is provided. Resampling is also used in inexpensive devices, so this problem can be considered solved in principle. Devices in the region of $ 30- $ 60 (sound cards) or stereos up to $ 600, generally similar in DAC to these sound cards, perfectly reproduce frequencies up to 10 kHz, tolerably up to 14-15, and somewhat way the rest. This is sufficient for most real music applications, and if someone needs more quality, they will find it in professional quality devices, which are not much more expensive, they are simply made with the mind.
