Sometimes it seems that audiophiles contribute more than any other group to that amazing collection of half-truths and outright hoaxes we collectively call urban legends. So after you hear the stories about gold-plated connectors, chemically pure or directionally sensitive speaker cables, or other forms of madness seemingly designed with the sole purpose of taking ever more money out of the gullible audiophile's wallet, it is understandable if you're skeptical about yet another of these urban legends: namely, that mixing noise to an audio source before it is digitized and copied onto a CD, for instance, actually improves sound quality.

Except that this is no urban legend. There are sound mathematical reasons as to why this actually works.

CD-quality audio uses 16-bit sampling. In other words, the amplitude of the audio signal is represented by a 16-bit number (actually, a little bit over 44,000 such 16-bit numbers every second.) The actual amplitude value can therefore be anything between 0 and 65535.

The ratio between the loudest and the quietest signal is 65535 : 1. Engineers who use decibels (dB) for everything would say that this is a little bit over 48 dB. It is important to realize that this is the signal amplitude, not its power; power varies by the square of the magnitude, just as with an electrical signal, twice the voltage means twice the current and four times the power across a constant resistance. So the signal's dynamic range in terms of its power is a little bit over 96 dB.

So what's with the noise? Well, first of all, you must realize that when you digitally sample a signal, you unavoidably add noise to it by virtue of the fact that the samples have limited resolution. Let's say, for instance, that at subsequent sample points the signal level was 1.3, 5.2, 4.4, 8.9. After the sampling, we get values of 1, 5, 4, and 9. But this, in effect, is equivalent to mixing a noise signal with values 0.3, 0.2, 0.4 and -0.1 to our original.

Another fact to consider is this: any signal whose level is under 0.5 will completely disappear after digitization. Such levels will always be rounded down to 0.

So what happens when we add white noise with a maximum amplitude of 0.5? As a result of this, signals with an amplitude below 0.5 may show up in the sample with an amplitude of 1 after all.

What this means, in effect, is that at the expense of slightly increased noise, we have extended the signal's dynamic range from 1-65535 to 0.5-65535. This factor of two shows up as 6 dB in terms of the signal's power, a not at all insignificant increase. This comes at a cost of course (you can't create something out of nothing, not even information): the signal-to-noise ratio is decreased by 6 dB.

I believe it is even possible to observe this effect with your own ears (no CD players involved.) On more than one occasion, I noticed that a faint, distant sound became more audible in the presence of an even fainter white noise in the background.