A new approach to spectral estimation from irregular sampling

This article addresses the problem of signal reconstruction, spectral estimation and linear filtering directly from irregularly-spaced samples of a continuous signal (or autocorrelation function in the case of random signals) when signal spectrum is assumed to be bounded. The number 2L of samples is assumed to be large enough so that the variation of the spectrum on intervals of width π/L is small. Reconstruction formulas are based on PNS (Periodic Nonuniform Sampling) schemes. They allow for reconstruction schemes not requiring regular resampling and suppress two stages in classical computations. The presented method can also be easily generalized to spectra in symmetric frequency bands (bandpass signals).