9

Fuzzy Aliasing

This chapter is dedicated to detailed studies of the aliasing processes observed in cases where the sampling operation is performed nonuniformly. It is shown that randomizing of sampling can attenuate the aliasing effect. The aliases are not taken out completely at this stage. Some aliasing related effects are still present but they are diffused and not so well defined as in cases of periodic sampling. The term ‘fuzzy’ fits well to this kind of aliasing as there are numerous multiple-frequency contributions to this kind of aliasing process. Various aspects of fuzzy aliasing are discussed. It is emphasized that successful elimination of aliases, crucial for high-performance digital signal processing at frequencies exceeding half the sampling rate, could be achieved only by a skilful combination of randomized sampling techniques with application of specific algorithms. Both the sampling and signal processing stages have to be arranged in the correct way. The signal processing algorithms provide resolution of the frequency-overlapping problem, which is made feasible by proper randomization of sampling. Some of these special algorithms for proper alias-free signal processing are described in Part 2 of this book.

As demonstrated in the following chapter, a clear insight into the processes underpinning fuzzy aliasing is an essential precondition for development of new techniques for signal processing, including hybrid algorithms and algorithms adapted to sampling nonuniformities. ...

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