Nonlinear Sampling and Lebesgue's Integral Sums

Details Nonlinear Sampling and Lebesgue's Integral Sums Nonlinear Sampling and Lebesgue's Integral Sums

2010-09-06

arxiv.org/abs/1009.1080v3

Physics

Data Analysis, Statistics and Probability

This is a continuation of my research of the classification of singular systems as linear and nonlinear (see IEEE CAS MAG, III

Scientific paper

We consider nonlinear, or "event-dependent", sampling, i.e. such that the sampling instances {tk} depend on the function being sampled. The use of such sampling in the construction of Lebesgue's integral sums is noted and discussed as regards physical measurement and also possible nonlinearity of singular systems. Though the limit of the sums, i.e. Lebesgue's integral, is linear with regard to the function being integrated, these sums are nonlinear in the sense of the sampling. A relevant method of frequency detection not using any clock, and using the nonlinear sampling, is considered. The mathematics and the realization arguments essentially complete each other.

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