Extended Sample Rates In The Ada-8Xr; Wordlength, Dithering And Prism Sound Sns (Super Noise Shaping); Truncation And Dithering - Prism Sound ADA-8XR Operation Manual

Prism Sound ADA-8XR Multi-channel A/D D/A Converter Operation Manual - Revision 1.00
When the '4x' sample-rates (176.4kHz and 192kHz) were first used, they were occasionally
interfaced in 'Four-wire' mode, i.e. with one channel spread across two AES3 carriers!
However, it was more common to use 'Two-wire' interfacing at a frame rate of '2x'.
The principle of using a low-rate interfaces to carry reduced channel-count at extended
sample-rates is now becoming widespread on interfaces other than AES3, such as MADI or
SuperMAC.

7.2.4 Extended sample rates in the ADA-8XR

The ADA-8XR operates internally at sample-rates up to 352.8kHz, with 192kHz being the
current maximum external PCM rate. It can also provide or accept 'one-bit' formats such as
DSD if required. In these matters, we are partly at the mercy of the market since, presently,
our own tests have yet to show that sample rates beyond 96kHz provide any audible
improvement over well-engineered 96kHz sampling. It is also our opinion that one-bit
representations would need to operate at bit rates significantly above those presently
proposed in order to match the quality of the ADA-8XR's current 24-bit/96kHz or 192kHz
output.
As with all Prism Sound products, the ADA-8XR can transact extended rates (88.2kHz and
above) in either 'one-wire' or 'two-wire' format. Since all input and output ports can be
individually defined, it can be used in mixed-format environments, or to convert either format
to the other. The ADA-8XR does not support 'four-wire' interfacing.

7.3 Wordlength, dithering and Prism Sound SNS (Super Noise Shaping)

7.3.1 Truncation and dithering

There are many points in a digital audio signal path where precision can be lost. For
example, in a digital transfer from 24-bits to 16-bits, or in an analogue to digital conversion.
In this situation it is not sufficient just to discard low-order bits – this causes truncation
distortion, characterised by aharmonic frequency components and unnatural, harsh decays.
Instead, it is preferable to use some sort of 'dithering' process, whereby the truncation
process is linearized by modulating the signal prior to the truncation, usually by the addition of
a small amount of noise. By adding a random element to the truncation decision, small
components as far as 30dB below the noise floor can be accurately represented, and an
analogue-like low-signal performance can be realised. This is achieved at the expense of
slightly raising of the noise floor, although with some dithering schemes such as noise-
shaping, linearization can be achieved with no noticeable increase in noise.
How can dithering allow information to be preserved below the least-significant bit? It seems
impossible. Consider a simple example where the audio samples are numbers between one
and six, and we are going to 'truncate' them (i.e. reduce their resolution) so that numbers from
one to three become zero, and those from four to six become one. Clearly much information
will be lost, and all excursions of the signal between one and three and between four and six
will not affect the output at all. But if we throw a die for each sample, add the number of spots
to that sample, and translate totals of six and below to zero and totals of seven and above to
one, we have a simple dithering scheme. Input samples of three will be more likely to result
in outputs of one than will inputs of one. The throw of the die is our dither noise. Since all the
faces of the die have an equal chance of occurring, this is known as 'rectangular probability
distribution function' (RPDF) dither, which in fact does not produce perfect linearization. We
actually use 'triangular probability distribution function' (TPDF) dither, which is like throwing
two dice with a resultant increase in the probability of medium sized numbers – totals of two
and twelve occur much less often than seven.
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