This concept develops the lattice filter structure in adaptive signal processing by formulating linear prediction within a Hilbert space of jointly stationary random variables, where prediction is expressed as orthogonal projection onto subspaces spanned by past or future samples. It defines pth-order forward and backward linear prediction errors as orthogonal-projection error operators, shows their variances are time-invariant under stationarity, and derives order-update (Levinson-type) recursions that express (p+1)th-order forward and backward errors in terms of pth-order errors via the partial correlation coefficient (parcor) and reflection coefficient. The domain is statistical/adaptive signal processing (Wiener filtering and its lattice realization), relating linear prediction theory to optimal filtering, Gram-Schmidt orthogonalization, and stability analysis of predictive filters.
This concept develops the lattice filter structure in adaptive signal processing by formulating linear prediction within a Hilbert space of jointly stationary random variables, where prediction is ex…