dCS 974 User Manual

Manual for Software Version 1.0x

dCS Ltd

May 2001

GENERAL TECHNICAL INFORMATION

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 PDF28 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.

28PDF = Probability Distribution Function. References to Rectangular Dither or Triangular Dither refer to the shape of the PDF of the dither.

Manual part no: DOC1241121A1

Page 104

Document No: OS-MA-A0124-112.1A1

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