Behringer DSP1100 User Manual page 22

sampling rate. The sampling rate determines the effective audio frequency range. The sampling rate must
always be more than twice the value of the highest frequency to be reproduced. Therefore, the well known
CD sampling rate of 44.1 kHz is slightly higher than twice the highest audible frequency of 20 kHz. The
accuracy at which quantization takes place is primarily dependent on the quality of the ADCs and DACs
being used.
The resolution, or size of a digital word used (expressed in bits), determines the theoretical "Signal to Noise
ratio" (S/N ratio) the audio system is capable of providing.
The number of bits may be compared to the number of decimal places used in a calculation - the greater the
number of places, the more accurate the end result. Theoretically, each extra bit of resolution should result in
the S/N ratio increasing by 6 dB. Unfortuanetly, there are a considerable number of other factors to be taken
into account, which hinder the achievement of these theoretical values.
If you picture an analog signal as a sinusoidal 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 traces a continuous curve, which very seldom coincides with the cross points of the
grid. A signal level at the sampling points will be assigned a digital value, usually the one closest to the exact
representation. This limit to the resolution of the grid gives rise to errors, and these errors are the cause of
quantizing noise. Unfortuanetly, quantizing noise has the characteristic of being much more noticeable and
unpleasant to the ear than "natural" analog noise.
Quantization Steps
Quantization Errors
(Noise)
Fig. 5.1: Transfer diagram for an ideal linear ADC (2´s complement represantation)
In a digital signal processor (such as the one in the FEEDBACK DESTROYER) the data will be modified in a
number of ways. In other words, various calculation 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
calculation 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 DSP in the FEEDBACK DESTROYER operates 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.
22
U (Voltage)
0000
1111
-8 -7 -6 -5 -4 -3 -2
1110
1101
1100
1011
1010
1001
1000
Digital Words
5. OPERATION
8
0111
7
0110
6
0101
5
0100
4
0011
3
0010
0001
1 2 3 4 5 6 7 8
-1
-2
-3
-4
-5
-6
-7
-8
Conversation Rate
Continuous
Analog Signal
t (Time)