23
E
amplitude into a numerical value, quantizing. The two actions together are referred to as digitizing.
In order to carry out the opposite the conversion of a digitized signal into its original analog form a Digital
to Analog Converter or DAC is used. In both cases the frequency at which the device operates is called the
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 as high as 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 digital word used (expressed in bits), determines the theoretical Signal/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. Unfortunately, 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 analogue 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 still 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. Unfortunately, quantizing noise has the characteristic of being much more noticeable and
unpleasant to the ear than natural analog noise.
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 (2s complement representation)
In a digital signal processor, such as the DSPs in the VIRTUALIZER 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 round-
ing 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 VIRTUALIZER 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. For 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 will start 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
4. TECHNICAL BACKGROUND
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