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dCS 974 User Manual Manual for Software Version 1.0x
dCS Ltd May 2001
Manual part no: DOC1241121A1
Page 104
Document No: OS-MA-A0124-112.1A1
Contact
dCS
on + 44 1799 531 999 email to: more@dcsltd.co.uk
(inside the UK replace + 44 with 0) web site: www.dcsltd.co.uk
G
ENERAL
T
ECHNICAL
I
NFORMATION
Word Length Reduction
Word length reduction (truncation) causes an error signal to be added to the
wanted signal. The error signal is usually referred to as “Q noise” or
Quantisation noise – the approximation is made that the errors are noise-like.
This is true for large signals, but for smaller ones it is not so. As the wanted
signal gets smaller, the complexity of the error signal decreases, and the errors
first of all pile into ever lower order harmonics or intermods, and then, as the
level of the signal sinks below the Q level, much error power piles into the
fundamental. This causes its amplitude to become unpredictable – it may drop
abruptly to zero and disappear, or it may cease to go down any more and just
stay at a constant level. From the audio viewpoint, this sounds very unpleasant.
As a signal tail decays away, the tonal quality changes, and then it decays into
distorted mush and either abruptly stops, or else keeps fuzzing away until a new
signal starts. The level at which all this happens is the lsb of the output word –
for CDs, it is at the 16 bit level, which equates to about -90 dB0. The level is
high enough to be quite audible, and the effect must be tackled to make
reasonable quality CDs.
There is really only one way of tackling the problem – another signal has to be
added to the wanted one to smooth the staircase transfer function that
truncation causes. Mathematically, with two signals present, the transfer
function the wanted signal sees is the convolution of the PDF
28
of the second
signal and the staircase function. The converse is also true – the transfer
function the additional signal sees is the convolution of the PDF of the wanted
signal and the staircase function. This aspect is not a problem with the dither
types considered below, but it can be with some highly frequency shaped
dithers.
The additional signal is usually referred to as dither, and it is usually noise-like,
because then its statistics can be controlled, and the converse effect of the
signal modulating the dither can be made insignificant, or zero. However, there
are a number of ways that this dither signal can be generated and treated. The
major options are:
• it can be generated from the signal or generated independently and added
(“Dither”). It seems implausible that the dither signal can be generated from
the signal, but it can, and this gives the lowest added noise power option. It
is noise shaping on its own, but there are some circumstances where it
needs help from additional dither.
• it can be added inside or outside an error shaping loop.
• it can be frequency shaped to match the ears response or not. We can use
techniques that suppress error energy in the areas where the ear is
sensitive, and put it in areas where the ear is not sensitive. Usually this
shuffling around process costs us – we remove a little from the sensitive
areas and add back rather more in the less sensitive parts, but that’s life.
We still gain some improvements.
The table below gives the actual noise levels for 16 bit truncated signals with no
dither, various dither types, noise shaping alone, and noise shaping with dither.
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PDF = Probability Distribution Function. References to Rectangular Dither or Triangular Dither refer to the
shape of the PDF of the dither.