This concept develops the recursive parameter updates that drive the lattice filter as an optimal linear predictor in adaptive signal processing, focusing on how the forward and backward prediction-error variances (sigma_p^2) and the cross-correlation quantity delta_p (the inner product between forward and backward prediction errors) evolve as prediction order p increases. It formalizes the projection-based (rather than error-based) view of linear prediction, defining the forward and backward prediction coefficients (a_{p,i} and b_{p,p-j}) as the optimal, order-dependent, time-invariant combiner coefficients obtained by projecting x[n] onto the subspace spanned by past or future samples, under the assumption of process stationarity. The domain is statistical/adaptive signal processing, and the concept relates to the broader theory of linear prediction, orthogonal projections in inner-product (correlation) spaces, and the reflection-coefficient (Levinson-Durbin-type) recursion that constructs lattice filter stages from the autocorrelation function of the process.
This concept develops the recursive parameter updates that drive the lattice filter as an optimal linear predictor in adaptive signal processing, focusing on how the forward and backward prediction-e…