Browsing by Subject "Uncertainty relationship"

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    Universal lower bound for finite-sample reconstruction error and ıts relation to prolate spheroidal functions
    (Institute of Electrical and Electronics Engineers, 2018) Gülcü, T. C.; Özaktaş, Haldun M.
    We consider the problem of representing a finite-energy signal with a finite number of samples. When the signal is interpolated via sinc function from the samples, there will be a certain reconstruction error since only a finite number of samples are used. Without making any additional assumptions, we derive a lower bound for this error. This error bound depends on the number of samples but nothing else, and is thus represented as a universal curve of error versus number of samples. Furthermore, the existence of a function that achieves the bound shows that this is the tightest such bound possible.