Uniform linear prediction of bandlimited processes from past samples (Corresp.)
J. Brown · IEEE Transactions on Information Theory · 1972
Forx(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 spacingTsatisfying0 < 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 ofx(t)is uniform in the sense that the coefficients\{ a_{kn} \}do not depend on the detailed structure ofx(t)but are absolute constants for any choice ofT. 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.