Title :
Nonlinear sampling and Lebesgue´s integral sums
Author :
Gluskin, Emanuel
Author_Institution :
Ort Braude & Galilee Sea Acad. Colleges, Karmiel, Israel
Abstract :
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, in two different versions. The mathematics and the realization arguments essentially complete each other.
Keywords :
transforms; Lebesgue´s integral sums; frequency detection; nonlinear sampling; physical measurement; singular systems nonlinearity; Clocks; Equations; Estimation; Frequency measurement; Quantization; Switched systems; Switches; Integral sums; Lebesgue´s Integral; Nonlinear Sampling; Nonlinear transform; Spectrum analysis;
Conference_Titel :
Electrical and Electronics Engineers in Israel (IEEEI), 2010 IEEE 26th Convention of
Conference_Location :
Eliat
Print_ISBN :
978-1-4244-8681-6
DOI :
10.1109/EEEI.2010.5662115