Digital Alias-free Signal Processing

4

Randomized Quantization

Quantizing is usually defined as a rounding-off operation and this definition fits both the deterministic and the randomized versions of this operation. The quantization process is always carried out according to the same generalized scheme, given in Figure 4.1. To quantize a signal, instantaneous values are first roughly measured and then the measurement results are rounded off. The differences lie in how in these procedures are implemented, leading to various properties of the quantized signals. While the signal instantaneous values are always measured by comparing them with some reference threshold levels, the latter are kept in fixed positions for deterministic quantizing and are randomly varied for randomized quantizing. This means that the rounding-off function in both cases is carried out in two different ways. It is deterministic in the first case and probabilistic in the second case. Realization of the second approach seems to be and usually is more complicated than the first. However, under certain conditions it pays to perform quantizing of signals in this more complicated way as the properties of the quantized signals are quite different, which leads to various potential desirable benefits. On the other hand, the errors of randomized quantizing are typically distributed in an interval that is twice larger than those of comparable deterministic quantization. Essentials, advantages and drawbacks of this quantization approach are discussed in ...