39
E
Quantization Steps
U (Voltage)
-8 -7 -6 -5 -4 -3 -2
Digital Words
1111
1110
1101
1100
1011
1010
1001
1000
0000
t (Time)
0001
0010
0011
0100
0101
0110
0111
Conversation Rate
8
7
6
5
4
3
1 2 3 4 5 6 7 8
-1
-2
-3
-4
-5
-6
-7
-8
Quantization Errors
(Noise)
Continuous
Analog Signal
Fig. 4.3: Sampling quantization error
If you picture an analog signal as a curve, then the sampling procedure may be thought of as a grid
superimposed on the curve. The higher the sampling rate (and the higher the number of bits), the finer the
grid. The analog signal is a continuous line which only meets the intersections of the grid exactly at very few
points. All other points on the line are at greater or smaller distances from the intersections. This limit to the
resolution of the grid gives rise to errors, and these errors are the cause of quantizing noise. This quantiza-
tion noise has the unfortunate characteristic of sounding much more unpleasant than "natural" analog noise
when highly amplified.
In a digital signal processor, such as the DSPs in the ULTRA-DYNE PRO, the data will be modified in a
number of ways. In other words, various calculations, or processes, will be done in order to achieve the
desired effect on the signal.
This gives rise to further errors, as these calculations are approximations, due to their being rounded off to a
defined number of decimal places. This causes further noise. To minimize these rounding errors, the calcu-
lations must be performed with larger data words than those of the audio data. This process is comparable to
a pocket calculator that performs its calculations with a greater number of decimal places than can be shown
on the display. The DSPs in the ULTRA-DYNE PRO operate with a 24-bit resolution. This is accurate enough
to reduce quantization noise to levels which are usually below the audible threshold. However, when using
extreme equalizer settings, some quantizing side effects may be detected.
Digital sampling has one further, very disturbing effect: its high sensitivity to overloads.
A simple sine wave will serve as our example. If an analog signal starts to overload, it results in the amplitude
of the signal reaching a maximum level, and the peaks of the wave starting to get compressed, or flattened.
The greater the proportion of the wave being flattened, the more harmonics, audible as distortion, will be
heard. This is a gradual process.
Digital distortion is quite different, as illustrated by this simplified example. If we take the situation where a
4<->bit word has the positive maximum value of 0111, and add to it the smallest possible value of 0001 (in
other words, the smallest increase in amplitude possible), the addition of the two results in 1000 - the value of
the "negative" maximum. The value is turned on its head, going instantly from positive max to negative max,
resulting in the very noticeable onset of extreme signal distortion.
4. TECHNICAL BACKGROUND