Derivatives of Periodic Sampling

It is not easy to benefit from application of nonuniform sampling and at the same time not to suffer from the negative effects that usually accompany processing of the signals sampled in this way. To make these anti-aliasing techniques practically applicable, the typical negative effects corrupting this kind of signal processing have somehow to be suppressed. A search for a good approach to this problem has led to the recent development of hybrid sampling methods, discussed in Chapter 10. They are based on the idea of mixing the elements of periodic and randomized sampling in order to gain from exploiting the advantages of both. The derivatives of periodic sampling discussed in this chapter are considered as essential building blocks for composing such hybrid periodic/nonuniform sampling models. Especially useful are periodic sampling point sequences with random skips. As shown in the following chapters, whenever this type of sampling procedure is used, the consequences of the sampling phase shifting have to be understood in order to take them into account. To reveal the essential relationships between the phase shifting of sampling and the sampled signal reconstruction conditions, it is desirable to visualize the involved signal transformation processes. To do this it is suggested that estimation of Fourier coefficients should be considered as a process rather than a calculation of a parameter and that this approach should be used to visualize ...

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