Weiss Enginering Ltd.
DAC501-4ch/DAC502-4ch
4.5
Digital level control and Dithering
Digital Level Control – done the right way. With sound examples.
In high-end HiFi 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 number can be up to 5 digits long (the sum 2
plus 3). As an example: 30 times 500 equals 15000. 2 digits times 3 digits yields a 5 digit result.
In digital audio, the numbers are represented in the binary system, not the decimal system. A decimal
number consists of digits 0 through 9, a binary number of digits 0 and 1.
So a binary number may look like this:
1011 0011 0101 1101
This is a 16 digit or 16 bit binary number, the grouping into 4 bit chunks is for better readability. The audio
samples on a CD are represented with such a binary number system with each sample value represented
with 16 bits.
Now let’s assume we have an 8 bit gain factor for a level control. If we apply that to a signal coming from a
CD we multiply an 8 bit gain factor with a 16 bit sample value. The result is up to 24 bits long (the sum of
the word-lengths of the two factors).
An example:
0100 1001 x 1001 0110 0111 1011 = 0010 1010 1110 1001 0001 0011
The question now is what do we do with the 24 bit long result? The digital to analog converter which converts
the samples after the level control may only be capable to handle 16 bit wide samples. Thus what should
we do with the excessive 8 bits? The simplest solution is to truncate the 24 sample to 16 bits, i.e. to cut off
the 8 less significant bits. The truncated 24 bit result above then would look like this:
0010 1010 1110 1001
i.e. the first 16 bits of the 24 bit result above. The remaining bits
0001 0011
are discarded. If these bits are discarded, an error is introduced. This error is called a quantization error,
because the 24 bit result is requantized to 16 bits.
Unfortunately the quantization error is part of the audio signal – and if we take that part away from the signal,
the signal undergoes some distortion, the so called quantization distortion.
The sound example at the link below shows how such a distortion sounds. In this music example a 16
bit signal is truncated to 8 bits. 8 bits in order to clearly show the effect. Notice how the noise (distortion) is
modulated by the music signal.
•
https://www.weiss.ch/linked/digital-level-control/nodither.mp3
This is how a badly implemented digital level control works....
Fortunately there is a better way to handle the re-quantizing. One solution would be to use a D/A converter
with a higher word-length, e.g. a 24 bit converter, to accommodate for the 24 bit samples coming out of the
level control. This of course would already help a lot, but there is another technique: dithering.
The idea about dithering is to de-correlate the quantization error from the audio signal. As we have seen in
the example above, the quantization error depends on the audio signal, i.e. it is correlated with the audio
signal. On the other hand, if dither noise is added to the 24 bit sample after the level control and before
the re-quantization to 16 bits, the quantization error can be fully de-correlated from the signal. This means
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