Quantization Noise Educational Example
Illustrates the use of the Wave Shaper block for quantizing the input audio signal. To appreciate the adverse effects of
quantization, the quantizer is here set to 16 quantization steps which corresponds to 4 bits (i.e. 2-to-the-power-of-4 distinct
amplitude levels to describe the signal). The noise introduced by this extreme level of quantization is readily
apparent. Although quantization noise is a non-linear signal dependent phenomenon, it can be modelled as an additive
zero-mean uniform stochastic process with an amplitude range from -Delta to +Delta where
Delta=V/Number_of_Quantization_Steps and where V equals the signal amplitude (nominally V=1). With this simple model,
it is straightforward to show that every additional bit in the quantization results in a 6dB improvement in
signal-to-quantization-noise-ratio.
Try increasing the number of quantization steps to appreciate the corresponding improvement in audio quality. At 65536
steps (i.e. 16 bits) the effects of quantization are almost inaudible. The signal-to-quantization-noise-ratio is improved by 72dB
compared with the 16-steps (i.e. 4 bits) case.
The in-built quantizing shaping function applies linear PCM coding to the signal. Try experimenting with different schemes
by designing your own shaping functions (e.g. using MATLAB) and importing them into the Wave Shaper via the file I/O
dialog box.
[Refs: (1) "The Computer Music Tutorial", Curtis Roads, The MIT Press, 1996. p 33.
(2) "Advanced Signal Processing and Digital Noise Reduction", Saeed V. Vaseghi, Wiley-Teubner, 1996. p 20.]
