Weiss Engineering INT204, Руководство пользователя

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number can be up to 5 digits long (the sum 2 plus 3). As an example: 30 times
500 equals 15 000; 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 a 8 bit gain factor for a level control. If we apply that to
a signal coming off a CD we multiply a 8 bit gain factor with a 16 bit sample
value. The result is up to 24 bits long (the sum of the wordlengths of the two
factors). An example:
0100 1001
×
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 bit sample to 16 bits,
i.e. to cut off the 8 least 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.
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 wordlength, 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
decorrelated from the signal. This means instead of distortion there is noise.
The music is undistorted. The audio example at the link below is again a 16 bit
signal quantized to 8 bits, but with dither noise added. A much more pleasant