Behringer DSP1200P - Manual (Page 28)

28
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. 4.1: Transfer diagram for an ideal linear ADC (2’s complement representation)
In a digital signal processor, such as the DSPs in the MODULIZER 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 off
errors, the calculations must be carried out with a higher resolution than that of the digital audio data being
processed (as a comparison, an electronic calculator may operate internally with a greater number of decimal
places than can be shown on its display). The DSPs in the MODULIZER PRO operate with a 24 bit resolution.
This is accurate enough to reduce quantizing 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: it is very sensitive to signal overload. Take the following
simple example using a sine wave. 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, the level of distortion as a percentage of the total signal rising with the increase of the input
signal level.
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.
4.2 Reverberation and reflection
In a concert hall the sound the listener hears comprises both the source signals (e.g. acoustical instruments,
P.A. system) and thousands of reflections of these "primary signals", which bounce off floor, ceiling and walls
to reach the ear after a short delay. These reflections represent thousands of echoes of the direct signal, which
are not perceived any longer as single echoes but - due to their sheer number - as reverberation. Basically, the
reflected signal portions reach the ear later than the source signal, and the very fact that they do not arrive from
the same direction as the direct signal (see fig. 4.2), makes it possible to hear “spatial information”, i.e. to
perceive the direct signal as it is “embedded” in the room acoustics.
4. TECHNICAL BACKGROUND