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

For either a deterministic or stochastic signal band-limited to the normalized frequency interval , explicit coefficients 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 satisfying ; that is, 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 is uniform in the sense that the coefficients do not depend on the detailed structure of but are absolute constants for any choice of . 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.