Signal Recovering Based on Fourier Analysis from Nonuniform Samples

This paper describes a new approach that can process nonuniformly sampled signals efficiently, in the sense the digital spectrum and signal recovering from nonuniformly sampled signal can be derived precisely. The results of research on estimation spectra of signals whose samples were taken at randomly distributed sampling instants are presented. The paper determines the conditions under which a discrete Fourier transformation spectrum estimator provides an unbiased approximation of the spectrum of the original continuous-time signal in an unlimited range of frequencies. In the research nonuniformly sampled signals is represented as the algebraic addition of impulse function. Based on the random theory, the expected value is obtained. The signal is recovered by the inverse Fourier transformation.