This concept covers the theory of linear prediction in discrete-time signal processing, including the lattice-filter formulation of order-recursive projections and the resulting minimum-phase property of forward linear prediction error polynomials, which is proved via orthogonality of prediction errors to the subspace spanned by past samples and a factorization argument showing all reflection coefficients (and hence polynomial roots) lie strictly within the unit circle. It further connects this to the Wold decomposition of a stationary random process into purely deterministic (line-spectrum) and purely nondeterministic (continuous-spectrum) components, and to parametric power spectral density estimation via pole-zero (ARMA), all-zero (MA), and all-pole (AR) models, establishing that the p-th order linear prediction coefficients of a process satisfying an AR model are identical to that model's autoregressive coefficients. The domain is statistical/digital signal processing, specifically linear prediction theory, lattice filter structures, and parametric spectral estimation, situated within the broader discipline of stochastic signal analysis and system identification.
This concept covers the theory of linear prediction in discrete-time signal processing, including the lattice-filter formulation of order-recursive projections and the resulting minimum-phase propert…