Digital Audio - Quantization

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Let's now take a step back to the sampled voltage we mentioned earlier. What we have is an electric signal which varies continuously; let's suppose we collect a voltage-sample which, in order for it to be converted into digital, must necessarily be approximated into an integer number seeing that we can't use infinite amounts of binary digits to represent it. We therefore need to choose and fix a set of criteria to carry out this approximation. The first operation consists in sub-dividing the voltage range of the signal into a set of sub-intervals for which a central point is located for each one. The next diagram illustrates this situation:

Digital Audio - Quantization operation

Quantization operation

The following notation has been employed: the samples are picked up at a constant rate (marked on the time axis t) and numbered (1, 2, 3...). The voltage axis is sub-divided into 8 intervals (A, B, C, D for the positive voltages and A', B', C', D' for the negative) and a central point has been located for each interval. Seeing that there are 8 intervals, we require 3 bit to represent them.

Table 18.5. Interval-representation by a 3 bit word 

IntervalAssociated binary word
A000
B001
C010
D011
A'100
B'101
C'110
D'111

Let's take the first voltage sample. As we can see, it drops at the C interval (010) therefore is represented by the central point of this interval. Sample 2 drops at interval D (011) and again, is represented by its central point. This procedure of representing the sample-values with the intervals' central points goes on until we stop the sampling process. The following table shows the values derived from the first 9 samples:

Table 18.6. Quantization example 

SampleRepresenting intervalRepresenting binary value
1C010
2D011
3D011
4A000
5B'110
6D'111
7C'111
8B101
9D001

So what we have done is: we've picked up voltage values from our signal at a constant rate, and we've converted them into a binary format, approximating them. Next we'll look at how this operation introduces an error into the reproduction of the wave-form.








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