Found this so far, its the artical Dan refers to in his white paper:
http://www.digido.com/dither.html have a look at 'Part II',
C&P from the link above:
Dither
How to Dither Let's look at that long sample word. Whether it's 24 bits or 32 bits, we have to find some way to move the important information contained in the lower (least significant) bits into the upper 16 bits for recording to the CD standard. Truncation is very bad. What about rounding? In our digital dollar example, we ended up with an extra 1/2 cent. In grammar school, they taught us to round the numbers up or down according to a rule (we learned "even numbers...roundup, odd...round down"). But when we're dealing with more numerical precision and small numbers that are significant, it gets a little more complicated.
It turns out the best solution for maintaining the resolution of digital audio is to calculate random numbers and add a different random number to every sample. Then, cut it off at 16 bits. The random numbers must also be different for left and right samples, or else stereo separation will be compromised.
For example:
Starting with a 24-bit word (each bit is either a 1 or a 0 in binary notation):
Upper 16 bits Lower 8
Original 24-bit Word MXXX XXXX XXXX XXXW YYYY YYYY
Add random number ZZZZ ZZZZ
The result of the addition of the Z's with the Y's gets carried over into the new least significant bit of the 16-bit word (LSB, letter W above), and possibly higher bits if you have to carry. In essence, the random number sequence combines with the original lower bit information, modulating the LSB. Therefore, the LSB, from moment to moment, turns on and off at the rate of the original low level musical information. The random number is called dither; the process is called redithering, to distinguish from the original dithering process used to during the original recording.
Random numbers such as these translate to random noise (hiss) when converted to analog. The amplitude of this noise is around 1 LSB, which for 16 bit lies at about 96 dB below full scale. By using dither, ambience and decay in a musical recording can be heard down to about -115 dB, even with a 16-bit wordlength. Thus, although the quantization steps of a 16-bit word can only theoretically encode 96 dB of range, with dither, there is an audible dynamic range of up to 115 dB! The maximum signal-to-noise ratio of a dithered 16-bit recording is about 96 dB. But the dynamic range is far greater, as much as 115 dB, because we can hear music below the noise. Usually, manufacturer's spec sheets don't reflect these important specifications, often mixing up dynamic range and signal-to-noise ratio. Signal-to-noise ratio (of a linear PCM system) is the RMS level of the noise with no signal applied expressed in dB below maximum level (without getting into fancy details such as noise modulation). It should be, ideally, the level of the dither noise. Dynamic range is a subjective judgment more than a measurement--you can compare the dynamic range of two systems empirically with identical listening tests. Apply a 1 kHz tone, and see low you can make it before it is undetectable. You can actually measure the dynamic range of an A/D converter without an FFT analyzer. All you need is an accurate test tone generator and your ears, and a low-noise headphone amplifier with sufficient gain. Listen to the analog output and see when it disappears (use a real good 16 bit D/A for this test). Another important test is to attenuate music in your workstation (about 40 dB) and listen to the output of the system with headphones. Listen for ambience and reverberation; a good system will still reveal ambience, even at that low level. Also listen to the character of the noise--it's a very educating experience.
Some Tests for Linearity
You can verify whether your digital audio workstation truncates digital words or does other nasty things, without any measurement instruments except your ears. Obtain the disc Best of Chesky Classics and Jazz and Audiophile Test Disc, Vol. III, Chesky JD111.* Track 42 is a fade to noise without dither, demonstrating quantization distortion and loss of resolution. Track 43 is a fade to noise with white noise dither, and track 44 uses noise-shaped dither (to be explained). Use Track 43 as your test source; you should be able to hear smooth and distortion-free signal down to about -115 dB. Then listen to track 44 to see how much better it can sound. Try processing track 43 with digital equalization or level changes (both gain and attenuation, with and without dither, if it's available in your workstation) to see what they do to the sound. If your workstation is not up to par, you'll be shocked. Use a quiet, high-gain headphone amplifier to help reveal the low level problems.
*available at major record chains or through Chesky Records, Box 1268, Radio City Station, New York, NY 10101; 212-586-7799. The hard-to-find CBS CD-1, track 20, also contains a fade to noise test.
So Little Noise, So Much Effect
-96 dB seems like so little noise. But strangely, engineers have been able to hear the effect of the dither noise, even at normal listening levels. Dither noise helps us recover ambience, but conversely it also obscures the same ambience we've been trying to recover! Dither noise adds a slight veil to the sound. That's why I say, dither, you can't live with it, and you can't live without it.
Improved Dithering Techniques
Where there's a will, there's a way. Although the required amplitude of the dither is about -96 dB, it's possible to shape (equalize) the dither to minimize its audibility. Noise-shaping techniques re-equalize the spectrum of the dither while retaining its average power, moving the noise away from the areas where the ear is most sensitive (circa 3 KHz), and into the high frequency region (10-22 KHz).