When I was asked to write this article, it was originally supposed to be about wordclock and the equipment available on the market for distributing it. However, as I was planning it, I realized that technological evolution moves so fast that it turns us users into mere consumers who often don't know why things are the way they are or where they come from. Because how many of us know what wordclock really is? What's more, how many of us know how digital audio works? What advantages and drawbacks does it have compared with analog? And how have those drawbacks been overcome?
As a result of this reflection, I decided to go a bit further in this article and give some basic notions of how all this works, so we can understand a little better what we have in our hands. The fact is that all of us, both those who work in professional studios and those who devote their free time to music or sound, rely to a large extent on equipment that processes audio in the digital domain: from a personal computer's audio card to the most sophisticated digital mixing console. All that travels through that equipment is 0s and 1s.
THE DIGITAL WORLD
The arrival of microprocessors and their later application in DSPs (Digital Signal Processors) made the development of computing possible and, with it, practical applications such as digital audio. By then we were already able to capture and store sounds for later playback by cutting grooves into records or magnetizing tapes. But these media were perishable and, with each playback, the quality decreased.
In addition, dynamic range and signal-to-noise ratio (our "Holy Grails") were limited by the physical properties of the materials used as media and by the technology itself.
Digital audio promised better dynamic range and signal-to-noise ratios. But it starts with a major handicap: the digitization or quantization of audio is done discretely rather than continuously; that is, only a certain number of samples are taken per unit of time and encoded as 0s and 1s. These samples are used to generate an approximation of the original sound which, of course, is never exact, but comes very, very close.
Without going into great detail, which is not the purpose of this article, quantization is defined by the number of samples taken per unit of time, or sample rate, and by the resolution or size of the word that stores the information (8, 16, 20, 24 bit). Since the computing system is binary, it is easy to deduce that with a resolution of 8 bits we can place the samples taken at one of 256 possible quantization levels (2^8=256). If the conversion system is 16-bit, there will be 65,536 levels (2^16), and at 24 bits 16,777,216 (2^24). To use an analogy from the world of digital photography, the same image of a landscape can be represented with 256 colors, 65,536 colors or more than a million of them. Pretty graphic, right?
THE NYQUIST THEOREM
Good, we now know that our digital system converts analog (continuous) sound into a discrete (discontinuous) representation of it based on taking samples. But how many samples should we take? At what resolution? The Nyquist theorem tells us that in order to sample an analog signal, the sample rate must be at least twice the highest frequency contained in the sound we want to reproduce.
Given the human audible range, which goes from 20 Hz to 20 kHz, the sample rate needed to be at least 40,000 samples per second. On the other hand, each bit in a sample adds 6 dB of dynamic range, so with 8 bits we would get 48 dB, with 16 bits 96 dB and with 24 bits 144 dB. Since the useful dynamic range (without reaching the threshold of pain) is about 110 dB and that of analog tape systems about 72 dB, quantizing at 16 bits initially seemed like a good solution. In addition, keep in mind that the more bits per word and the higher the resolution, the more space is required to store the information. And that space costs money.
All these theoretical figures are, however, lower in reality, due to physical phenomena that occur in the digitization process and that Mr. Nyquist didn't warn us about.
ALIASING
In any complex sound, such as that produced by a stringed instrument, the frequencies generated can go beyond 20,000 Hz in the form of harmonics which, although inaudible to us, are present. When a sound containing frequencies higher than those that can be encoded, according to Nyquist, is digitized, the phenomenon of aliasing occurs, converting those unquantizable frequencies into others that can be quantized but are not present in the original sound, which introduces undesirable artifacts.
The clearest image for understanding aliasing is to recall what happens when we see a wagon wheel in a western: although the wagon is moving forward, we see the wheel turning backward. There is a mismatch between the wheel's rotation period and the "sampling" rate of film (24 frames per second). To avoid this problem, a low-pass filter has to be added that cuts above the frequency corresponding to half the sample rate. This filter is known as an anti-aliasing filter. Since a theoretical low-pass filter with an infinite slope does not exist and, in addition, such filters cause phase shift problems at frequencies near the cutoff (equally undesirable), the sample rate was standardized at 44,100 Hz so that filters with a gentler slope from 22,050 Hz could be used.
QUANTIZATION ERRORS
Another problem we encounter, inherent to the digitization system, is that when a sample's amplitude does not match a value that is a multiple of 6 dB, the bit it occupies is resolved by proximity, which introduces constant rounding that adds distortion. This is especially audible (and therefore unpleasant) in very low-amplitude passages (reverb tails, very soft passages of an instrument…).
It is not only digitization that adds these quantization errors. Once the signal has been digitized, we perform all kinds of operations: we mix tracks, apply plug-ins, change gain, etc. All these processes are carried out with mathematical operations that cause individual samples to be rounded to the nearest bit, adding the resulting distortion. The solution, paradoxically, is to add a certain type of digital noise at very low levels, so that it is mainly this noise that gets removed in the rounding process. This process is known as dithering, and it adds the minimum level of digital noise needed to minimize rounding problems.
The results of dithering algorithms can be improved with noise shaping techniques, that is, by adding the noise in the areas where the human ear is less sensitive, making the added noise practically inaudible. It is important to point out that, although in theory we should apply dithering to every process subject to quantization errors, in practice the noise present in the recording chain is adequate enough to serve that purpose. Moreover, the programs on the market usually apply it every time a process is performed on the signal (normalization, plug-ins).
It is especially advisable not to use normalization except at the very end, once we have completely processed the material, since we must keep in mind that each time we do it, we raise both the signal level and the noise level and, on top of that, add new noise with the dithering applied. It really is a mistake we should avoid. One process where applying dithering is extremely recommended is when reducing the resolution of material, for example from 24 bit to 16 bit. There are some highly prestigious processors on the market with surprising results: Apogee's UV22, the POW-r Consortium's POW-r or Waves Audio's IDR.
As a tip, whenever possible I recommend working at 24 bit, from recording right up to producing the mastered file. The increase in dynamic range makes the noise introduced by quantization errors truly negligible. Dithering would only need to be applied when converting the master file to 16 bit for CD.
JITTER
Samples are taken according to the sample rate, fn samples per second. This means that, in theory, the time interval between samples should be 1/fn seconds. In practice, this is not always the case, which introduces a third type of distortion: the one that depends on wordclock errors, known as jitter.
Wordclock is a clock signal that travels along with the digital audio signal (although it can also travel separately) and sets the timing for when samples must be processed, both in recording and playback. When samples are slightly late or early relative to the moment they should be processed, they alter the frequencies they encode, producing fluctuations or modulations somewhat analogous to those that occur on a tape when its speed is not constant. It is a very subtle effect, hard to describe, but it shows up as a loss of definition and a poorer stereo image.
A digital system with a good external clock unit that supplies wordclock and synchronizes all the equipment is the best guarantee against this problem, especially at the A/D conversion stage. Afterward, the samples can be "repositioned," but they will no longer represent the sampled reality, and we will carry the unwanted effect throughout the entire chain.
CONCLUSION
A lot of water has passed under the bridge, as they say, since the first digital equipment appeared. Little remains of those units so many professionals reviled for their cold, crunchy sound. Their Achilles' heels have been discovered one by one and solutions have been found. Technological development is moving unstoppably toward systems with higher sampling capacity and greater resolution; the media for storing such amounts of information are advancing at the same pace and, just as importantly, at ever more affordable costs. New consumer formats are appearing that take advantage of these developments and put impressive levels of fidelity in consumers' hands.
In light of all these considerations, and perhaps a little out of context, two very different questions come to mind. The first is: does this evolution mean the end of analog systems? I say no; the harmonic distortion generated by tube equipment and the very pleasant compression produced by tape recording systems still have, and will continue to have, a place in the chain of a hybrid system, from the sound source to the playback device. For the second I have no answer: what good is so much sonic excellence if the audio format that seems set to prevail is a compressed format (with a loss of information of around 90%) that will be listened to on equipment that is, at best, mediocre?
