Background Analysis

      Now let's do some probing analysis. Why should any CD improvement devices be able to change the sound of CDs at all, especially by making analog modifications to them? After all, the CD medium is intrinsically digital, and thus should be inherently immune to analog influences, either for the better or for the worse (for example, analog scuffing and scratches from rough handling of the CD surface are not supposed to make the sound any worse, as they would have with analog vinyl LPs). Furthermore, the digital CD medium promised perfect sound forever, and you can't improve on perfection (any change from perfection must by definition be a worsening).
      Let's first look into the background of CD tweaks, and then we can learn why today's analog improvements can indeed improve the sound of a digital medium.
      Ever since the dawn of perfect sound forever, audiophiles yearning for better music have sought ways to improve the sound of CDs. Perhaps we were simply to dumb to be persuaded by the professional engineers who assured us that CD was necessarily audibly perfect, since it had flat bandwidth to the 20 kHz limit of human hearing, and it had a 96 dB signal/noise ratio and corresponding resolution approaching the limits of human hearing, and it had negligible measured distortion. Or perhaps we didn't buy that glowing promise of perfect sound, since some of us heard sonic flaws in digital, and also heard that analog tape and analog vinyl still surpassed CD in some ways.
      Bob Stuart of Meridian probably deserves credit for being the first to invent a CD tweak that actually made a difference. He found that you could change, and in most cases improve, the sound of a CD by simply stacking a second CD on top of the one whose underside was being read by the laser.
      This empirical finding was somewhat useful for the sonic improvement it wrought at the time. But the scientific and logical implications of this empirical finding were even more important. Why? Because the mere fact that the sound of a CD could be changed meant that bits were in point of fact not bits, and therefore that the CD medium was necessarily imperfect and furthermore was subject to the whims of motley external factors, including analog factors and tweaks to counter those factors (much as vinyl playback had been and continues to be).
      As we have come to understand the digital medium better in the years since its introduction, we have come to understand many things about it that we naively overlooked or assumed during its nascence. These new lessons were discussed and explained at length in IAR issues 43-45, 55, 58, 61-62. Now, let's discuss four key lessons, which are especially relevant to improving the sound from your CDs.

Re-Creating the Two Dimensional Music Signal

      One lesson is that our digital media are actually half analog. If you look at any music waveform, you'll note that it's plotted on a two dimensional graph, with the vertical axis being amplitude and the horizontal axis being time. It should be intuitively obvious that if you distort either of these two axes you will distort the music waveform.
      Most people intuitively believe that this two dimensional music waveform is stored (in digital form) on the CD medium, and the only task faced by the CD playback unit is to merely read an already existing music waveform (in digital form) off a CD and convert it to analog. But the truth is very different. In truth, the CD playback unit is actually responsible for literally freshly creating the entire two dimensional music waveform, which it then outputs to the rest of your system.
      For one of these two waveform dimensions, the vertical amplitude axis, the CD contains some information, but the data coming from the CD are emphatically not fully or adequately descriptive of the music waveform's ever changing amplitude, especially for musical frequencies above 2 kHz or so. Instead, these data coming from the CD are only sketchy clues about the music waveform's ever changing values along the vertical amplitude axis. Thus, your CD playback unit obtains only sketchy clues about the waveform amplitude from the CD, and it is the CD playback unit which is responsible for literally creating the vertical amplitude axis of the two dimensional music waveform (as opposed to merely reading the complete amplitude data from the CD). After reading the sketchy amplitude clues from the CD, your CD playback unit must intelligently interpret these sketchy clues, fill in the blanks, and re-create the best approximation it can to the original music amplitudes (using its aptly named reconstruction filter, perhaps with the addition of some sort of averaging algorithm to enhance resolution and accuracy) - all before converting the amplitude information to analog, to be output to the rest of your system.
      Even for the amplitude dimension, the sketchy information coming off the CD is not digital, but is actually analog in form, as we shall discuss below. Thus, your CD player is really fully responsible for freshly creating all digital information about the amplitude axis. Its first job is to read the sketchy clues about the amplitude axis in analog form from the CD and convert these sketchy clues to a digitally representative format (which by the way is still carried as an analog signal waveform throughout the digital circuitry). Its second job is to flesh out these sketchy amplitude clues into a form that fully represents the amplitude axis for each discrete sample.
      But now, what about the other dimension of the music waveform, the horizontal time axis? Is its data stored on the CD in full? No. Then, is its data stored on the CD as sketchy clues, in the same way that the amplitude axis data was stored? No.
      We have seen that (in today's digital systems) the vertical amplitude axis of the music waveform is encoded digitally from an analog input signal, is reduced to sketchy clues, and is recorded onto a storage device (like a CD). Then your playback unit reads this sketchy vertical amplitude axis information as analog, then interprets and effectively converts it to digital (about which more below), then re-creates and re-constructs it to flesh out all the amplitude information, and finally re-converts it back to analog (obviously a very complex process). But the other half of that same music waveform, its horizontal time axis, is not encoded digitally onto the recording, neither in full nor as sketchy clues. And it is not even encoded onto the recording in analog. Actually, it is not encoded onto the recording at all! Instead, it is merely assumed.
      A CD playback unit, for example, assumes that the CD was recorded with its time axis marching along at an exact rate of precisely 44,100 samples per second. The CD playback unit therefore generates a brand new clock running as close to a constant 44,100 samples per second as it can, and it uses this fresh, newly generated time clock to read, regenerate, and reconstruct  the incoming amplitude-only data from the CD.
      You might say that a CD contains only ¼ the data required for the two dimensional music waveform, half of the amplitude data required to plot the vertical axis and none of the time data required to plot the horizontal axis.
      The CD player literally creates or generates the two dimensional music waveform, using the amplitude-only data from the CD for the vertical amplitude axis and its own internal freshly generated clock for the horizontal time axis. Thus, the internal circuitry of the CD playback unit is totally responsible for "recording", i.e. creating and generating, one whole dimension of the two dimensional music waveform, the horizontal axis (as well as being responsible for accurately interpreting the amplitude clues that came off the CD, to correctly construct the vertical amplitude axis). Obviously, if there are even the slightest irregularities or distortions in its freshly internally generated time axis, then the two dimensional music waveform will be distorted.
      Now, this time dimension is inherently analog, or continuous, rather than discrete. We call a system digital if the amplitude dimension is discrete and represented by a digital coding system. But the other half of the music's two dimensional waveform, the time dimension, flows continually. A digital system is supposed to perform its manipulations at discrete time points, corresponding to the sampling intervals. But there can be an error in the exact point in continuously flowing time that these discrete time points occur.  These errors are inherently analog in nature. That is, the digital circuitry could be any analog fraction of time early or late in performing its manipulations. As you may know, there are error checks (parity checks) in digital systems to help insure that the discrete amplitude data is free from errors. But there is no parity check for time errors. And, since the CD playback unit is fully responsible for generating this time dimension, this half of the two dimensional music signal, there is no check or correction for such time errors that are an analog fraction of a sampling time period early or late.
      As discussed previously in IAR, any time error committed by your playback units that gets propagated to the DAC chip will distort the music waveform just as badly as an amplitude error would. Just a few picoseconds of time wander or jitter at the input to the DAC chip can cause an effective amplitude error as bad as the amplitude error from losing a whole bit of amplitude data (the exact relationship depends on the system resolution in bits, the sampling or oversampling rate, and the frequency of the music signal being reproduced at the time). If your CD playback unit reconstructs the music waveform with the correct amplitude but at the wrong time, then it will be distorting your two dimensional music waveform as surely as if it picked the wrong amplitude to reconstruct at the right time.

Digital Circuitry is Actually Analog

      A second lesson is that the internal circuitry of your CD player and D-A convertor might be called digital circuitry, but in reality it is actually analog circuitry. This was previously discussed at length in IAR issue 45. The popular misbelief is that all this digital circuitry is mistake proof, and generally uncorruptible by outside influences, since it handles digital bits that are either on or off, and each given segment of the digital circuitry (e.g. a flip-flop) is either on or off. But if we probe inside each digital circuit segment or element, and examine its innards on a close-up or microscopic internal level, to find out how it really works inside, we discover that each digital element is actually an analog circuit. For example, a bistable flip-flop, the basic element that holds a 0 or 1, is actually an analog circuit, a circuit which changes from a 0 to a 1 at an analog voltage threshold and/or at an analog point in time. Even the master clock circuitry, the fountainhead of digital authority that governs all the other digital circuitry, is itself actually analog. The part of the clock circuit that sends the square wave waveform to other circuits is itself analog, the part that generates the square wave waveform is itself analog, the part that tracks the crystal is analog, the crystal itself is an analog mechanical resonator, and of course the clock's square wave waveform is an analog waveform.
      Incidentally, if we were to look even more microscopically at all this digital circuitry that is actually analog, we might get to the point where we see quantum jumps in electron states. But these quantum jumps are discrete, not digital. In other words, the discrete quantum jumps do not carry any digital representation. Instead, the discrete quantum jumps merely additively contribute in an analog fashion to the ultimate analog voltage or current that they en masse constitute as an aggregate. Also, each of these discrete quantum jumps is individually random, so we would hardly want to depend on random entities for any reliable digital representation.
      Now, analog circuits are notoriously susceptible to corruption by external influences. And since so-called digital circuits are in fact analog circuits, they too are susceptible to corruption. Corrupting external influences can easily change the precise voltage or current at which these analog circuits detect a sufficient threshold to change their digital state from 0 to 1 (or vice versa). And, likewise, corrupting external influences can easily change the precise timing moment when these analog circuits change their digital state. Even very small unwanted changes in precise timing and/or in precise voltage or current levels can produce distortion of your music signal.
      For example, you might think that 1% electronic part tolerances are precise, but if an external influence makes the current in a D-A convertor change by merely .0015%, that can cause distortion as great as losing a whole bit of information in a 16 bit system. Many of the better CD playback units employ 20 bit A-D convertors, to take advantage of digital upsampling and averaging enhancements to resolution just ahead of the A-D convertor; here an unwanted current change of less than .0001% could cause distortion as bad as losing a whole bit of information. And the new 24 bit systems are even more susceptible to external influences, if their full resolution is to be realized without distortions.
      Similarly, if external influences cause timing changes in the precise analog moment that a threshold is reached, which makes a so-called digital (actually analog) circuit change its digital state, then that timing change, when it reaches the DAC chip, can cause distortions in the final re-creation of the music signal by that DAC chip (as we discussed above). Your CD playback units have numerous circuits that depend on specific, precisely constant relationships between time and current (or voltage). Often capacitors are involved, which take a certain precise time to charge to a certain level, provided the charging current is predictably, precisely constant. If an unwanted external influence modulates the current so it's not predictably, precisely constant, then that influence will also be modulating the timing of the signal and/or the circuit's switching actions, and thereby could distort your music signal.
      When a so-called digital circuit switches its digital state at the wrong analog threshold and/or at the wrong analog moment in time, it effectively commits two crimes. It loses some of the true musical information that should have been there, and it also adds distortion to your music (distortion that might well sound ugly, because it is probably not harmonically related to the music).
      What are some of these external influences that can cause unwanted changes in currents, voltages, and timing? Consider the servos that are constantly moving, to allow the laser to track the typically wobbling, eccentric CD. These servos require a lot of current, and their current draw is not constant, but instead varies quite a lot. For example, a bad, sharp CD warp, requiring a sudden large burst of current to track, might well occur just at one point during each rotational revolution of the CD, so once per revolution there would be a sudden spike of current draw for that servo. When that servo draws a big spike of current, then the voltage and/or current available for all the rest of the circuits suddenly and temporarily drops. This is turn could cause the so-called digital circuits to reach their analog switching threshold at a different level and/or at a different time, thereby losing information and adding distortion to your music. Thus, a sharp CD warp could cause a burst of distortion once per revolution of the disc. Sound familiar? That's exactly the same problem you experience from vinyl LPs, where a sharp warp sends a sudden loud burst of spurious bass energy demand through your system, which distorts your music by sapping current and via intermodulation distortion mechanisms (especially in your woofer). The more things change, the more they stay the same. A vinyl LP and turntable system are as analog as you can get, yet here we see that a so-called digital system is vulnerable to the same kind of analog problems and is susceptible to the same kind of analog external influences. So a digital system is not only vulnerable (instead of being immune) to external influences, but it is also vulnerable in an analog way to analog external influences.
      The specific problem of servos causing distortion, by drawing spikes of current as they track the real world non-perfect molded polycarbonate disc that is a CD, is so severe and obvious that makers of more expensive CD players have worked to attack and reduce this problem. When you buy an expensive CD player, some of the extra parts budget you're paying for has probably gone into beefier, higher quality power supplies that sag less under the demand of high spikes of current from servos, or even into separate power supplies for the servos vs. for the digital circuitry that is vulnerable to analog influences. These costly measures surely help, but they probably can't provide full immunity from servo current drain, because of the incredibly small tolerances required by a high resolution digital system. Even a beefy power supply with a low source impedance would have a tough time keeping voltage and/or current levels constant within .0015%, when there's a sudden spike of current demand by a tracking servo, as a 16 bit system requires. And even separate power supplies usually work off a common power transformer and common power cord, which have a series source impedance that affects the precise constancy of voltage and/or current levels under dynamic conditions.
      Consider too that nearly all of today's more expensive CD players also boast another feature, 20 bits of effective resolution from CD, with a 20 bit D-A convertor. But this common premium feature puts the CD player back to square one with its premium power supply, because now the power supply must hold current levels constant within less than .0001% (16 times more stringent performance), if it is to realize full 20 bit resolution without distortion (and we have measured that humans can hear down to at least 21 bits of resolution, so you could hear distortion of that 20^th bit).
      If the slightest amount of external vibration reaches the CD player's laser tracking system, then the servos will have to work harder to fight this externally induced vibration, so they can track the CD pits in spite of it. The servos will draw bursts of current in synchronism with the frequency or periodicity of the vibrations, and so, if these current draws do cause distortion, then the distortion of your music will be modulated by these vibrations - a classic case of intermodulation distortion. These unwanted external vibrations could be mechanical vibrations coming from vibrating floor or wall mounts supporting the CD player, and/or they could be airborne vibrations that cause the chassis cover of the CD player to vibrate, and/or they could originate (or sympathetically resonate) within the twirling hard plastic disc itself.
      You can see why a host of tweaks have sprouted up to address this vibration problem, and why all of them make a sonic difference (not necessarily a sonic improvement, but the fact that they make any difference at all to a supposedly immune digital system is what's remarkable). There are special feet, special shelves, damping pads for chassis covers, damping mats for the CD itself, CD clamps, CD rings, etc. In fact, Bob Stuart's original tweak of adding an extra CD doubtless made its sonic

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