Performance of fir adaptive filters using recursive algorithms

Adaptive digital filters used for speech and data processing are investigated. The algorithms use either a least mean square recursively in time. Only the all-zero transversal and lattice filter structures are considered. A geometric or Hilbert space formalism is used to derive the LMS lattice, LS lattice, and "Fast" Kalman algorithms in a cohesive manner. Convergence properties of the LMS adaptive lattice filter are discussed. A deterministic model for multistage convergence is described which gives filter coefficient mean-values an output mean squared error as functions of time. The model is then extended to the LMS and LS lattice joint process estimators and to the "Fast" Kalman algorithm. In each case calculated curves obtained from the model are compared with simulation results. The performance of each adaptive predictor in the context of adaptive differential pulse code modulation of speech is compared.