Spectrum estimation of nonuniformly sampled signals

Nonuniform sampling of signals, if properly used, may allow performing digital signal processing that does not suffer from the undesired effects of aliasing. This paper presents the results of research on estimating spectra of signals whose samples were taken at randomly distributed sampling instants. The paper determines the conditions under which a DFT-like spectrum estimator provides an unbiased approximation of the spectrum of the original continuous-time signal in an unlimited range of frequencies. It also provides analysis of the accuracy of such spectral estimation and identifies factors which decide the quality of the results. Not every random sampling scheme is suitable for performing alias free signal processing. The analysis presented here shows how to generate two suitable sampling schemes. Numerical examples illustrate the main thesis of the paper.