Measurement scale for non-uniform data sampling in N dimensions

Abstract

A method for sampling a signal for signal processing, such as calculating the coefficients of a Fourier or other transform of the signal. The sampling occurs at sampling points which are the union of sets of points, each set being points separated by regular intervals of 1/pn where pn is a prime number. Where the signal is not accurately reconstructed from the sampled values the method recurses and increases the set of distinct primes. The invention relies upon the incommensurate nature of different primes to prevent the invention from degenerating into an inefficient sampling technique such as using regular intervals would provide. The scale, termed a D scale, is applicable to problems in diverse domains such as signal processing, including digital signal processing (DSP), image processing, scientific and engineering computational applications, data acquisition and statistical data analysis. Algorithms are provided that process an N dimensional Fourier and other kernel transforms of a multi-dimensional function using the non-uniform samples of the D scale along with Fast Fourier Transforms.

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