Weiss Engineering INT204, Owner'S Manual

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7
What is dithering? Suppose a digital recording has been made with a 24 bit
A/D converter and a 24 bit recorder. Now this recording should be transferred
to a CD, which has just 16 bits per sample, as you know. What to do with
those 8 bits, which are too many? The simplest way is to cut them off, truncate
them. This, unfortunately, generates harmonic distortions at low levels, but
which nonetheless cause the audio to sound harsh and unpleasant. The harmonic
distortion is generated because the eight bits, which are cut off from the 24 bits,
are correlated with the audio signal, hence the resulting error is also correlated
and thus there are distortions and not just noise (noise would be uncorrelated).
The dithering technique now is used to de-correlate the error from the signal.
This can be achieved by adding a very low level noise to the original 24 bit signal
before truncation. After truncation the signal does not show any distortion
components but a slightly increased noise floor. This works like magic — the
distortion is replaced by a small noise which is much more pleasant. I have given
the example of a 24 bit recording, which has to be truncated to 16 bits. Where
is the application in High-End Hi-Fi audio? More and more signal processing is
implemented in the digital domain. Think of digital equalizers, digital volume
controls, upsamplers, digital pre-amplifiers, decoders for encoded signals on DVD
etc. All those applications perform some mathematical operations on the digital
audio signal. This in turn causes the wordlength of the signal to be increased;
an input signal to an upsampler may have a wordlength of 16 bits (off a CD),
but the output signal of the upsampler may have 24 bits or even more. This
comes from the fact that the mathematical operations employed in such devices
increase the word length. A multiplication of two 2-digit numbers results in
a four-digit number. So after the upsampler the word length may be higher
than the subsequent processor may be able to accept. In this example, after
the upsampler there may be a D/A converter with a 24 bit input word length
capability. So if the upsampler generates a word length of more than 24 bits it
should be dithered to 24 bits for maximum signal fidelity.
Another application where dither is important is described in the next
paragraph.
1.4 Digital Level Control
In High-End Hi-Fi circles a level control done in the digital domain is often
viewed as being inferior to one operating in the analog domain. Let’s look on
how a digital level control works and why it can be an excellent solution if it is
properly implemented.
A level control is a multiplication of the audio signal with a constant, the
,,gain factor“. The gain factor usually is in the range of zero (signal fully off)
to one (signal untouched). A factor of 0.5 then means that the audio signal is
attenuated to half of its amplitude. What exactly happens when we multiply
two numbers? If we e.g. multiply a 2 digit and a 3 digit number, the resulting