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6.6 The basics of digital signal processing
To convert continuous analog signals into a series of digital words, a so-called Analog to Digital Converter
(ADC) is used. The converter functions by viewing the signal entering it a given number of times over a period
of time, e.g. 44100 times per second, giving a rate of 44.1 kHz, and in each case measuring the signal
amplitude, and giving it a numerical value. This form of measuring the signal regularly over a period of time is
known as sampling, the conversion of the 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 (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 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 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
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. 5.1: Transfer diagram for an ideal linear ADC (2´s complement represantation)
In a digital signal processor (such as the one in the VIRTUALIZER) 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,
6. OPERATION
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