Digital Sound Page 2

Dr. Lagadec supports his thesis with a very simple analysis of what happens when changing level in the digital domain and the nature of the attendant requantization error. This function is considered perhaps the simplest and best-understood type of digital signal processing. However, he has discovered a previously unknown form of error created by this simple processing: the digital gain control's transfer function (difference between input and output signals) varies according to the amount of gain or attenuation. The nature of the transfer function's non-linearity (imprecision), introduced by changing gain in the digital domain, is determined by the gain pair ratios; ie, the relative beginning signal level and the signal level after gain reduction. I won't go into the details here: the phenomenon is explained and documented fully in the paper.

This discovery is extraordinary for two reasons. First, it vindicates those who have long maintained, after critical listening, that digital faders affect sound quality (footnote 5). Second and more important, it reveals that even the simplest aspects of digital audio that are thought to be well understood are, in fact, not well understood. Dr. Lagadec has worked for the past 7 of his 17 years in digital audio in the area of digital level control, yet recognized and began researching this phenomenon during only the past year. Again, I quote Dr. Lagadec's paper: "It is remarkable that such a simple system, eminently amenable to the methods used in non-linear dynamics, has not—to the author's limited knowledge—been widely publicized yet. If an element of surprise can come from analyzing such simple systems, more instructive surprises may be in store when more complex ones are scrutinized."

With this last sentence, Dr. Lagadec implies that a digital Pandora's Box may be opened by closer analysis of other aspects of digital audio. Like the Pandora's Box of Greek mythology that contained the world's troubles, this digital Pandora's Box may reveal other problems in digital audio that no one knew existed. An understanding of these cracks in conventional digital audio theory will go a long way toward correlating listeners' subjective impressions with objective fact.

The paper then examines dither, another area which, like digital gain adjustment, is considered a closed subject because it is well understood. Dr. Lagadec presents a hypothesis which states that dither should be optimized based on the ear's short-term perception of quantization noise, rather than the current mathematically based long-term analysis: "Needless to say, the 'optimal' dither types in the long-term statistical sense which have been proposed by Vanderkoy [sic] and Lipshitz (footnote 6) are a very valid first approach. As they are, however, independent of any practical detector model, it is not unfair to expect further improvements in perceived performance from dither models optimized in a different, less mathematically rigorous, and more perceptually oriented way."

With that analysis, Dr. Lagadec again proposes that an existing precept, thought to be immutable, is in fact far from a settled question. Moreover, one can infer that future research should be based on improving perceptual qualities rather than conforming to mathematical theories. This is reflected in the phrases "independent of any practical detector model" (my interpretation: "without regard for human hearing"), and "dither models optimized in a different, less mathematically rigorous, and more perceptually oriented way." (emphasis added)

Significantly, this suggests that the criterion for what is considered optimum dither should be based on human hearing rather than on purely mathematical ideas or measurements that have little relation to auditory perception (footnote 7). This represents a remarkable shift in thinking away from the scientific dictum that measurements and theory are more reliable and important than human perception in determining "what is good" in music reproduction. The human perceptual element in audio engineering has long been disregarded because it cannot be quantified. The ability to measure and quantify an entity are the criteria by which science judges that entity's reality. The scientific mind tends to mistrust anything than cannot be represented or communicated by linear symbols. These symbols that describe reality, obtained by measurement and calculation, assume a greater importance than, or are even mistaken for, the actual reality they try to represent. It is thus momentous that one of the world's foremost audio scientists has called for accepting musical perception directly rather than in the abstract, linear terms of representational thinking.

Dr. Lagadec points to some future directions in digital audio, including "a much greater word length" than the current 16-bit system, and bandwidth much wider than 20kHz. This additional bandwidth would be "kept open for, say, low-level harmonics, harmonics due to non-linear processing, and out-of-band noise shaping." An advantage he notes of having bandwidth beyond 20kHz "would be the freedom to disregard the arguments as to whether there is perceptible sound beyond 20kHz." However, he notes that "For economic reasons, it is evident that hardware capable of such parameters at an acceptable cost is not for this decade."

This concept of today's digital audio being in its infancy and subject to radical changes in fundamental precepts is in sharp contrast to the prevailing view among most academics that the 20kHz bandwidth is adequate, and that properly dithered 16-bit representation provides sufficient resolution and dynamic range. Indeed, the idea that today's digital audio parameters are perfectly satisfactory for music were expressed by Dr. Stanley Lipshitz parenthetically in his "Tutorial on Phase," given at the convention. He somewhat derisively scolded critics of digital audio for speciously (in his view) blaming today's digital audio's fundamental parameters (he specifically mentioned sampling rate and word length) as the cause of its inferiority (in the critics' view) to analog.

Dr. Lagadec then says that since the previously unknown aspects of digital audio he has discovered correlate to what critical listeners have been saying for years, perhaps other claims of audible differences should not be dismissed so cavalierly by the audio engineering establishment, despite the lack of scientific proof of such differences. I was astonished by the paper's last paragraphs (quoted below), in which Dr. Lagadec expands his thesis by bringing up the subject of audible differences between cables. Claims of differences between cables have long been a bugaboo of audio engineers. Further, he contends that if no measurable differences exist between cables, yet critical listeners report such differences, perhaps our understanding of human hearing acuity is suspect, rather than the rationality of those who hear differences.

The paper concludes by calling for the world's audio scientists and researchers to vigorously pursue these new challenges and to make room for, rather than exclude, the role of listening in advancing audio science. Dr. Lagadec writes:

"The industry is full of lore as to the superior sound quality of some cables, connectors, electronic devices, and the like. Assuming, as scientists presumably should, that things can only sound different if they cause signals to become different, and using the technology available today to ascertain whether differences do exist, and if so what they consist of, we may hope to achieve reproducible improvements; to deepen our understanding of sound quality; and to separate unfounded legends from justifiable improvements.

"Conversely, if we were to discover that, when, say, different cables are used, the signals look the same beyond the resolution of today's best converters, but still sound reproducibly different, then we would indeed still have much to learn about human audibility.

"The advanced tools available today—the recorders, computer software, workstations, DSP chips and boards, monitor systems, A/D and D/A conversion systems, instrumentation—and which are within reach of any university might be put to use, scientifically, aggressively, to find out how we hear, and how we might improve what we hear. Every generation since Edison's days has said that its sound recordings were almost better than the original, and at the very least indistinguishable from reality. Ours will hardly be an exception, neither in hubris and hype, nor in the disappointment. Yet we have tools for generating and manipulating signals, moving them in space and time, which few of our predecessors dreamed of. The tools deserve to be used, and our engineers deserve to be guided, by scientists who will advance the state of the art ahead of the state of the industry."

Although the tenets put forth in "New Frontiers in Digital Audio" are hardly new to audiophiles, the paper is revolutionary to the mindset of the audio engineering community. What makes this paper such a significant and extraordinary event is the credibility and influence of its author. You may be certain that Dr. Lagadec does not speak lightly or from a shaky platform. Consequently, the ideas expressed in the paper will be given serious consideration by those accustomed to attacking the very same ideas when espoused by those of us without Ph.Ds.

As I considered the paper's ramifications, I couldn't help thinking about the people who for years have reported sonic anomalies in digital audio, only to be met with skepticism and ridicule. This is especially true of Doug Sax, who was one of the first and most outspoken critics of digital. During the past eight years, he has reported his listening experiences to an indifferent world. Despite his pre-eminence in the field of record mastering, he is regarded as a pariah by the audio engineering community for his views, views which I believe have been taken a step toward scientific fact by "New Frontiers in Digital Audio."

If "genius" is defined as the arriving at conclusions ten years before the rest of the world reaches those same conclusions, then both Roger Lagadec and Doug Sax, disparate as their approaches are, certainly qualify. The fact that Dr. Lagadec's paper may cause the audio engineering establishment to take seriously the listening impressions of people like Doug Sax is small consolation to music lovers who must listen to inferior CDs made during the period between when the problems were first reported (1982) and when the problems' existence were proved in a scientifically acceptable method (1990).

"New Frontiers in Digital Audio" holds out the hope that one day digital audio may exceed analog's performance in all respects. It is my sincerest hope that our successors regard today's pronouncements of digital audio's quality with the same combination of humor and incredulity with which we view Anna Case's assessment of Mr. Edison's machine.



Footnote 5: As did Doug Sax, the co-founder of Sheffield Lab who runs The Mastering Lab, a disc-cutting and CD master-tape preparation facility in Hollywood, CA. In an interview with JA, published in the October 1984 issue of HFN/RR> and later in the mastering industry magazine One-on-One, Doug maintained that "When you go through a digital editor...the loss is traumatic. You go in apples, you come out oranges." See also my interview with him in Vol.12 No.10.—Robert Harley

Footnote 6: Vanderkooy, J. and Lipshitz, S., "Dither in Digital Audio," Journal of the Audio Engineering Society, Vol.35 No.12, December 1987.—Robert Harley

Footnote 7: To be fair to the Lipshitz and Vanderkooy position on dither, their recent research and that of some of their students has been toward developing the idea of relating the spectral shape of the dither noise to the manner in which the ear's sensitivity varies with frequency. In other words the noise will have very little content between 1kHz and 4kHz, where the ear is very sensitive, but considerable more above 10kHz, where its audibility is reduced. This idea was most recently discussed in a paper presented at the 1990 Los Angeles AES convention, "Psycho-Acoustically Optimal Noise-Shaping" by Robert A. Wannamaker, available as preprint #2965 (Session Paper #F-I-5). Note, however, that the character of the shaped dither noise is still treated in a long-term statistical manner.—John Atkinson

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