Power spectral measure and reconstruction error of randomly sampled signals

We say that a signal is randomly sampled when the samples are taken at random instants of time. The study of random sampling and randomly sampled signals is motivated both by practical and theoretical interests. The first one includes spectral analysis (estimation of spectra from a finite number of samples) and quality of service (signal reconstruction), and the second one includes statistical analysis of reconstruction methods. The present paper focuses on the computation of the (theoretical) spectrum of randomly sampled signals and on the computation of the reconstruction error. Using a point process approach, we obtain general formulas for spatial random sampling, providing powerful tools for the analysis and the processing of randomly sampled signals.