Convergence behavior of non-equidistant sampling series
Signal Processing
Approximation of wide-sense stationary stochastic processes by Shannon sampling series
IEEE Transactions on Information Theory
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For x(t) a wide-sense stationary random process possessing a power spectral density S(@w) band-limited to -@p = @p, then S"*|sin@?@pt|^2@p^2(1N"1+32+1N"2+32)@?@?"N"""1","N"""2(t)@?S^*|sin@?@pt|^2@p^2(1N"1+1N"2) for S"*=min@?@w@?[-@p,@p]S(@w)andS^*=max@?@w@?[-@p,@p]S(@w), where |t|@?12. (ii) If there exists an r with 0 @pr (''guard-band'' assumption), then @?"N"""1","N"""2(t)@?8|sin@?@pt|^2@p^2(1+cos@?@pr)@?E[x^2(t)]@?[1N"1+1N"2]^2 for S"*=min@?@w@?[-@p,@p]S(@w)andS^*=max@?@w@?[-@p,@p]S(@w). These results generalize to random processes earlier work of J. B. Thomas and others on the problem of estimating truncation error for deterministic band-limited signals.