On Causal Estimation From Bandlimited Stationary Sequences

This paper considers the problem of estimating a stationary sequence ${bf y}$ from the observation of a stationary correlated sequence ${bf x}$ by means of a causal linear filter. Thereby, it is assumed that the spectral density $Phi_{{bf x}}$ of ${bf x}$ vanishes on a subset of the unit circle of positive Lebesgue measure such that the classical derivation of the estimation filter, based on the spectral factorization of $Phi_{{bf x}}$, can not be applied. The paper derives the transfer function of such an estimation filter, discusses its stability behavior, and applies the result to the causal reconstruction of deterministic signals from its samples.     «

This paper considers the problem of estimating a stationary sequence ${bf y}$ from the observation of a stationary correlated sequence ${bf x}$ by means of a causal linear filter. Thereby, it is assumed that the spectral density $Phi_{{bf x}}$ of ${bf x}$ vanishes on a subset of the unit circle of positive Lebesgue measure such that the classical derivation of the estimation filter, based on the spectral factorization of $Phi_{{bf x}}$, can not be applied. The paper derives the transfer function...     »