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Robust prediction of band-limited signals from past samples (Corresp.)

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For a complex-valued deterministic signal of finite energy band-limited to the normalized frequency band |w| \leq \pi explicit coefficients {a_{kn}} are found such that for any T satisfying 0 < T \leq 1/2 , \left| f(t)-\sum ^{2n}_{k=1}a_{kn}f(t - kT)\right| \leq E_{f}\cdot \beta ^{n} where E_{f} is the signal energy and \beta \doteq 0.6863 . Thus the estimate of f(t) in terms of 2n past samples taken at a rate equal to or in excess of twice the Nyquist rate converges uniformly at a geometric rate to f(t) on (- \infty , \infty ) . The suboptimal coefficients {a_{kn}} have the desirable property of being pure numbers independent of both the particular band-limited signal and of the selected sampling rate 1/T . It is also shown that these same coefficients can be used to estimate the value of x(t) of a wide-sense stationary random process in terms of past samples.

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Information Theory, IEEE Transactions on  (Volume:32 ,  Issue: 3 )