Zen & The Art of D/A Conversion Page 2

Yes, I know---there are tens of thousands of happy CD player owners. But you should now start to see why there are subjective shortcomings. Take the first assumption, that the signal had no components above half the sampling frequency. Real music inconveniently has a spectrum that extends up and up, well above the traditional "20 to 20k" audio bandwidth. Before it can be sampled, the music signal has therefore to be viciously filtered to avoid the particularly audible nasties of "aliasing"---such a benign word to describe one of the more unpleasant-sounding distortions---and the design of such filters is no trivial task. They ring; they produce gross phase shift in the audio band; they go out of alignment; if they have major ripples in their passband's amplitude response, these inconveniently show up in the digital domain as pre- and post-echoes (a phenomenon described by its rediscoverers, Roger Lagadec and Thomas Stockham, as "dispersion"); and, most important, the only way around these problems costs money---lots of it.

If only the CD sampling rate were higher than 44.1kHz, the digital recorder's input anti-aliasing filter problems could at least be moved farther away from the music, which is the real reason why the sampling frequency is too low.

I'll draw a discreet veil over the "perfect" A/D converter and data storage required---I live in hope.

The rest of the process you get for free when you buy a CD player. The perfect D/A converter---see my comment on its A/D equivalent. Of one thing I am sure: you can't buy one for the kind of money available to a manufacturer marketing a CD player for $349, let alone $149.

How about some of the minor impossibilities? The fact that the pulses coming from the DAC should be infinitely narrow turns out not to present a major problem. Even if the pulse is so broad that it lasts until the next one, producing a "staircase" waveform, the only effect is to droop the treble somewhat, about 4dB at 20kHz, the kind of problem that circuit designers are good at solving. The fact that the pulses should be spaced exactly 1/s seconds apart turns out to be much more serious. As pointed out by Philip Greenspun in the Winter 1986 issue of The Computer Music Journal, and discussed by Bob Stuart in Stereophile (Vol.9 No.2), any minor inconsistency in timing---due, say, to jitter in the player's crystal-controlled clock from heavy current demands on an inadequate power supply---means losing precision in the reconstruction of the fine detail of the analog signal. Engineers call this "distortion."

Now that you've accepted the fact that the existence of a precognitive reconstruction filter is an impossibility, look at the measured impulse response of a Philips-system CD player (fig.5). Familiar, huh? It turns out that one of the beauties of a signal once it is in the digital domain is that the direction of time flow no longer is an invariable constant. There is no reason at all why the music data on a CD can't be played from end to beginning, decreasing entropy and causing the musicians to grow younger. Some musical works---Barry Manilow's entire output, for example---might even sound better! Similarly, consider the steady flow of data through a CD player's circuits. Animal fanciers could consider the numbers as goats passing through a door; unless the doorkeeper had X-ray vision, he would not know anything about a particular goat until it passed through the door. However, there is no reason at all why the doorkeeper couldn't place a second door before the first and take some action at the main door based on what he found out at the second: stop all brown goats from going through, for example. To an outsider not aware of the existence of the upstream door, it would appear that the doorkeeper possessed prescience of the color of approaching but unseen goats.


The effect of being able to examine a stream of digital data anywhere along its length---provided you have enough RAM to hold that data---is the ability to be able to manipulate time; precognitive circuitry becomes a possibility. A filter operating in the digital domain can be made to approximate perfect behaviour because it can look both back and forward in time and operate on the current sample according to what it finds. In fact, this is the practical basis of digital filtration. The cost of RAM chips will never fall so low that the filter will be able to operate from minus infinity to plus infinity, but it can, in practice, ignore the contributions to the wave shape of samples far away in time from the current sample, as the resultant error in amplitude will be less than the random changes due to noise.

The digital filter used by the first generation of Philips players used 96 coefficients---it could examine 96 samples before and after the sample of interest simultaneously, in order to act as an ideal low-pass filter---while the new filter in the true 16-bit players has more, reaching further toward a better approximation to that perfect impulse response. This attempt to approach the theoretical elegance is one reason why audiophile-quality CD players, or at least CD players with pretensions to audiophile sound, feature the Philips D/A chip set, which includes the "precognitive" digital filter. (A perhaps more important reason is that Philips will actually sell their technology to small hi-fi companies.) Digital filters are now also appearing in players from Sony and Technics, some four years after the Dutch engineers at Philips formulated their system.

Now, are 16 bits sufficient? And what about oversampling? And the quality of the analog circuitry?

Footnote 1: I can't remember the name of this substance. A free year's supply of Stereophile to the first reader who can jog my memory. Or send me an aqueous solution.

hollowman's picture

(Correct me as necessary...)

The "low-pass filter" in JA's above discussion is not the "oversampling digital filter" (which is, in all reality, optional) nor is it the SAME as the output low-pass filter (e.g., analog, multi-pole).

Rather, the "low-pass filter" in JA's above discussion, is a mathematical (on-paper, or theoretical) concept of digital-to-analog RECONSTRUCTION.

To put it plainly, if all you had was a bare-bones DAC chip (take one of the first-generation CD players with a chip like Philips TDA1540) -- so, no oversampling -- the above discussion of "low-pass filter", and (sin x)/x curve and impulse response would STILL apply.

I think the confusion comes from the rather liberal way the term "reconstruction filter" is used. I.e., sometimes used as an alternate to oversampling (e.g, 4x, or 8x) ... as well as the textbook terminology (as JA notes above), or here...


(Wiki seems to suggest that the RF can ALSO be the output analog filter, e.g., brick-wall, multi-pole, etc. AFTER the DAC chip)

Again I might stand well corrected!!