Sampling Methods for Processes
Instead of observing a complete segment of a process on an interval, it is evidently desirable to consider suitable subsets, preferably countable ones, if they present the essential characteristics of the process on the bigger segment. A basic result in this direction for second order processes is the one due independently to Kotel’nikov and Shannon, and we present some results of this type for the stationary as well as some general processes, in Section 1. The work will be specialized to its band-limited and analytical aspects in the following two sections. Further a detailed analysis on periodic sampling, which is often used in engineering applications, is discussed in Section 4 along with an extension to random fields on ℝ n as well as a brief account to indexes of LCA groups. Some remarks on optional sampling of processes are included in the next section. As in the preceding chapters, the final complements section is devoted to further important results with detailed sketches. Most discussion is conducted on second order continuous parameter processes.
KeywordsRandom Field Covariance Function Vector Measure Order Process Discrete Subgroup
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