Let us study quantization concept by following example. Fig. 1 shows the electronic waveforms of a typical ADC. Here, figure 'a' is the analog audio signal to be digitized. The block diagram includes two sections, namely the sample-and-hold (S/H), and the analog-to-digital converter (ADC). In fact, the sample-and-hold is required to keep the voltage entering the ADC constant while the conversion is taking place. Moreover, breaking the digitization process into these two stages is an important theoretical model for understanding digitization (Smith 1999).
As shown by the difference between 'a' and 'b', the output of the sample-and-hold is allowed to change only at periodic intervals, at which time it is made identical to the instantaneous value of the input audio signal. Changes in the input signal that occur between these sampling times are completely ignored. That is, sampling converts the independent variable (i.e. time) from continuous to discrete.
Then, as shown by the difference between 'b' and 'c', the ADC produces an integer value for each of the flat regions in 'b'. So, quantization converts the dependent variable (i.e. voltage) from continuous to discrete. ...
It is essential, that the sampling and quantization degrade initial audio signal in different ways, as well as being controlled by different parameters in the electronics.
Let us consider the effects of quantization. Any one sample in the digitized signal can have a maximum error of LSB (least significant bit). The quantization error 'd' can be found by subtracting 'b' from 'c'. It means that the digital audio output 'c' is equivalent to the continuous input 'b' plus a quantization error 'd'. So, the quantization error can be interpreted as somewhat like random noise. In other words, quantization results in the addition of a specific amount of random noise to the signal. This additive noise is uniformly distributed between LSB, has a mean of zero, and a standard deviation of LSB.
Example. Passing an analog audio signal through an 8 bit digitizer adds an rms noise of , or about of the full scale value. A 12 bit conversion adds a noise of: , or about . A 16 bit conversion adds , or about .
It is obvious, that the number of bits determines the precision of digitized audio data. Digitizing this same signal to more bits would produce virtually no increase in the noise, and almost nothing would be lost due to audio signal quantization. How many bits are needed It depends from how much noise is already present in the analog signal, and also from how much noise can be tolerated in the digital signal (Smith 1999).
Small amplitude or slowly varying audio signals require enormous bit-depth for digitization. This problem can be solved by so-called dithering technique. At this case, a small amount of random noise is added to the analog audio signal. Appropriate circuits for dithering can use PC to generate random numbers, and then pass