Kega writes:

chung wrote:

Kega (myself) wrote:


Note also that I have not in my reasing involved dithering and other
techniques to increase the quality in a 16 bit PCM at low signal values.


But you HAVE to consider dithering, which is a key part of PCM systems.
Dithering effectively transforms the quantization errors, from being
correlated to the signal, to noise. So you can't say that at lower input
levels, the harmonic distortion increases because the step sizes are
now relatively large.

In a properly dithered system, you do not see the harmonic distortion
terms. The system is linear, with a slightly higher noise floor.


Now I'm getting curious. You see back in 1977 when I studied PCM (and
Adaptive PCM, Delta Modulation etc..) they (the teachers) never
mentioned dithering. It was first after CD arrives on the scene I heard
about it.

Kent,

The basic university professor may not have been aware of it back
then.

From what I have been able gather, Robert Wannamaker's PhD thesis
is a landmark paper on the entire subject. Of course it gets deep, but
he does a pretty good job of explaining things before he gets into
the depth. He also has an excellent section on the history of quantization
in chapter one. Essentially he credits L.G. Roberts as the first one to
use dither (in video) back in 1962. The thesis is freely available at:

http://audiolab.uwaterloo.ca/~rob/phd.html

I know slightly what it is (to add a kind of low level noise to trigg
the A/D-converter to differ between 2 samples that has close values).

That is about as intuitive as it gets, and is right on.

But how does it work?

Do you have different dither spectrum and level depending on the level
of the signal? (or depending of the spectrum of the signal itself,
etc...) For instans when level is sufficient high you don't need any
dithering, do you.

To answer your immediate question, yes, you do even for high-level signals.
To see what happens if you don't dither, write a quick Matlab script that
generates a perfect (at least to double-precision floating-point) sine wave,
quantize it to 16 bits, and look at the resulting spectrum. You'll see lots
of nasty spurs.

The business of examining dither involves the study of random signals
(AKA random processes or stochastic processes). There are two main
properties of a random process: 1) the amount of correlation from one
sample to the next (or between one time t1 and another t2 for a continuous
random process), and 2) the distribution (pdf, or probability density
function) of the process. It is property 1 we are describing when we
call a dither signal "white."

Rob shows that an nRPDF (the sum of n rectangular PDFs) white dither
will decorrelate the first n moments of the quantization error
spectrum from the input signal. In practice, n = 2, and 2RPDF is also
known as TPDF, or triangular PDF. So that means the first moment,
or the DC correlation, is removed, and also the second moment, which
is the so-called noise power modulation.

Hope this sparks some understanding/interest.
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
, 919-472-1124