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Uniform linear prediction of bandlimited processes from past samples (Corresp.)

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1 Author(s)

For x(t) either a deterministic or stochastic signal band-limited to the normalized frequency interval \mid\omega \mid \leq \pi , explicit coefficients { a_{kn} } are exhibited that have the property that begin{equation} lim_{n rightarrow infty} parallel x(t) - sum_{1}^n a_{kn} x(t - kT) parallel = 0 end{equation} in an appropriate norm and for any constant intersample spacing T satisfying 0 < T < fac{1}{2} ; that is, x(t) may be approximated arbitrarily well by a linear combination of past samples taken at any constant rate that exceeds twice the associated Nyquist rate. Moreover, the approximation of x(t) is uniform in the sense that the coefficients { a_{kn} } do not depend on the detailed structure of x(t) but are absolute constants for any choice of T . The coefficients that are obtained provide a sharpening of a previous result by Wainstein and Zubakov where a rate in excess of three times the Nyquist rate was required.

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IEEE Transactions on Information Theory  (Volume:18 ,  Issue: 5 )