Fourier Analysis of Time-Stamped Signals Using a Small Number of Samples

This paper concerns the Fourier analysis of measurements taken at times that are not at all uniformly spaced yet accurately known. Such can be the case when measurements are obtained by networked sensors with accurate or synchronized clocks using common Internet Protocol (IP) networks or other networks that do not make guarantees as to timely delivery of data. A method of computing a complex spectrum from a minimal number of samples taken at non-uniform time intervals is described. The novelty of this work lies in the method's ability to minimize the number of samples that must be acquired while still ensuring a desired level of signal-to-noise. A practical application of the method lies in doing spectral analysis of signals obtained from networked sensors where acquiring each sample is expensive in time, power, or money and so the number of samples taken is to be minimized. The method has been tested on actual measurements taken via smart sensors connected to the Internet.