Alias-free randomly timed sampling of stochastic processes

摘要: The notion of alias-free sampling is generalized to apply random processes x(t) sampled at times t_n ; said be alias free relative a family spectra if any spectrum the can recovered by linear operation on correlation sequence \{r(n)\} , where r(n) = E[x(l_{m+n}) \overline{x(t_m)}] . actual need not known effect recovery Various alternative criteria for verifying are developed. It then shown that whatsoever \{t_n\} Poisson point process positive (or negative) half-axis. A second example provided finite interval periodic (for t \leq t_o or \geq ) in which samples randomly independently skipped (expunged), such average rate an arbitrarily small fraction Nyquist rate. third shows jittered free. Certain related open questions discussed. These concern practical problems involved estimating from imperfectly \{ \}