Digital Alias-free Signal Processing

5

Pseudo-randomized Quantizing

Some of the effects caused by the deliberate injection of randomness into signal digitizing procedures are beneficial and some are harmful, increasing statistical errors. Fortunately, the targeted benefits are often obtained at low levels of randomization. Therefore the randomization level should be controlled to suppress additional errors and excessive randomization must, of course, be avoided in all cases. Yet another useful approach to obtaining the desirable effects is substitution of randomization by making deterministic signal digitization processes simply irregular. Such an approach is less harmful and usually leads to obtaining the same positive effects that are expected from the randomization. Pseudo-randomization of quantizing, considered in this chapter, actually represents such an irregularization. Pseudo-randomized quantizing is evidently a fully deterministic process. A description of it in probabilistic and statistical terms is a convenient way to explain that. It is further shown that skilful application of pseudo-randomization techniques leads to quite good results.

5.1 Pseudo-randomization Approach

It may be a little confusing to understand where the line separating randomized and pseudo-randomized quantization should be drawn. To randomize or pseudorandomize quantizing, an element of randomness either has to be added at the input of the used ADC or it has to be used for randomizing the positions of the reference threshold levels ...