Music & Fractals Page 2

This fact was brought home to me some eight years ago, when I bought Ry Cooder's Bop Till You Drop CD (Warner Bros. 03358-2), which was recorded in 1979 with an early 3M digital machine. The opening guitar figures to "I think it's going to work out fine" have a distinctively comb'n'papery sound; the somewhat granular background noise can be heard to "pump," changing its tone quality with the level of the guitar---a classic description of quantization distortion, the distortion that accompanies signals that have been converted to digital with too few bits. That 3M machine used 16-bit encoding, so in theory, there were enough bits to describe the signal without audible quantizing distortion. What had gone wrong?

As the story goes, the guitar had been recorded at too low a level at the original sessions, so when the time came to mix the digital multitrack to stereo, the engineer raised the level of the guitar track just as he would have done with an analog multitrack master. But if you record at too low a level with digital, the result is as if you had used an A/D converter with a fewer number of bits---one bit less for every halving of signal level. The result is that quantization distortion that should have remained below the threshold of audibility on the original is rendered audible by the engineer's gain adjustment, an adjustment that carries no resolution penalty with analog.

To show this point graphically, I used a Heath storage 'scope to capture a 20ms fragment of J. Gordon Holt's voice from the Stereophile Test CD with 8-bit precision. The reconstructed waveform, synthesized from 256 distinct levels, is shown in fig.1. I then reduced the analog level by a factor of eight, or 18dB, recaptured Gordon's voice with the storage 'scope, then multiplied the digital data by eight to give the same waveform level as before (shown in fig.2), effectively the same process as had happened with the Ry Cooder recording. The reduction of 18dB in signal level is equivalent to reducing the resolution of the 'scope by 3 bits, quantizing the signal with 32 discrete levels rather than 256. As can be seen from the squared-off appearance of fig.2 compared with fig.1, bringing up the level of the digital signal by 18dB---multiplying each data word by eight---doesn't increase the resolution of detail as it would do with an analog signal; rather, it just makes the limited 5-bit resolution more noticeable.

Fig.1 J. Gordon Holt's speaking voice, encoded with 8-bit precision (20ms time window).

Fig.2 J. Gordon Holt's speaking voice, encoded with 5-bit precision at the same overall level as in fig.1 (20ms time window). Ignore the additional asymmetry, which is coincidental.

But this is an extreme example, I'm sure you're thinking. Digital audio is not quantized with 5- or 8-bit resolution. We're talking sixteen bits here. Remember, however, that 16-bit quantization for a digital system is not the optimum for sound reproduction. It is just what could be routinely and relatively inexpensively achieved ten years ago when the CD specification was frozen. Listening tests at that time had shown that the human ear could detect the quantizing distortion from a linear digital system operating with less than 14-bit precision, and even 14 bits, as used in the first generation of video-based PCM processors, was found to be a little too close to the limit of what was acceptable. The adoption of 16-bit words therefore allowed four times the resolution of amplitude detail compared with 14-bit, and pushed the unnatural, unmusical effects of quantizing below the threshold of hearing.

It is a minimum standard, however, and any compromise, as with the example using Gordon's voice above, renders it audibly unacceptable. The problem with 16-bit digital recording as compared with analog, defined some years ago by Decca's Tony Griffiths, one of the UK's digital pioneers, is that there is effectively no "professional headroom." You have to know everything you might want to do to the signal before you commit yourself to the fundamental analog/digital conversion. If you discover at a later date that you want to increase the level, or edit in the digital domain, or add equalization, or even mixdown the digital multitrack to stereo, every one of those operations will lose resolution, the ultimate result being that what should have remained below the threshold of hearing---the non-fractal structure of the digitally reconstructed waveform---will be brought into the full light of day.

This, I believe, is why so many CDs sound unmusical compared with even 30-year-old analog recordings. The CD specification may say "16-bit encoding," but after all the postproduction processing has been carried out, it is quite possible that the inherent resolution of the data on the disc is 13-bit or even less. Larry Archibald always used to ask why CDs were so unmusical when J. Gordon Holt's PCM master tapes sounded wonderful. It is the unmasking of the digital system's unmusical background distortion (footnote 4) by the CD production process that answers that question, in my opinion. Add to that the effect of datastream jitter in the player or decoder, which itself reintroduces the equivalent of quantizing distortion, and it is surprising that CDs can sound musical at all.

The last effect, that of jitter, is said to be rendered less harmful by the various CD tweaks that are being promoted. In my postscript to Robert Harley's article on CD tweaks last May (Vol.13 No.5, pp.90-91), I described the results of experiments I had done to examine the nature of the noise floor of the final analog signal when a CD had been treated by having its edge coated with CD Stoplight. Although proponents of the "Bits is bits" school of audio engineering insist that nothing can be done to improve the quality of the data signal retrieved from the CD---remember that though this signal represents digital data, it is in fact an analog signal---I found that as well as repeatable changes in the shape of the noise floor adjacent to a recorded tone, CD Stoplight appeared to lower the overall noise floor slightly. As these effects are at the limit of hearing, perhaps they help the recovered analog signal to be reproduced with more of the original, pseudo-fractal crink! liness. Remember, too, that those who have reported on the subjective improvement wrought by these tweaks say that the sound becomes more realistic, more analog-like.

Footnote 4: An important difference to make between analog and digital systems. In an analog system, the background consists of random noise, uncorrelated with the musical signal. In a digital system, there is absolute silence when there is no signal; but when there is a signal, the background consists of harmonic and non-harmonic distortion products that are related causally to that signal. This is why the correct use of dither is so important. As well as increasing the digital system's resolution of fine detail, it renders what would otherwise be signal-related distortion products much more like the natural noise background of an analog system.
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