PERFORMANCE OF FIR ADAPTIVE FILTERS USING RECURSIVE ALGORITHMS

Adaptive digital filters used for speech and data processing are investigated. The algorithms of interest use either a least mean square (LMS) or least squares (LS) criterion and adapt the filter coefficients recursively in time. Only the all-zero transversal and lattice filter structures are considered. These types of algorithms have numerous applications including channel equalization; however, application to speech waveform coding is emphasized. 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 subsequently discussed. First-order expressions for single-stage convergence time and output mean squared error are obtained. A simple deterministic model for multi-stage convergence is then described which gives filter coefficient mean-values and output mean squared error as functions of time. Results obtained for the LMS lattice are also extended to the LS lattice. The model of convergence for the LMS lattice (predictor) 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.;Finally, an empirical comparison is made between the performance of each adaptive predictor in the context of adaptive differential pulse code modulation (ADPCM) of speech. A novel configuration consisting of an LS lattice predictor combined with a least squares lattice pitch detector to remove pitch redundancy is also tested. Our results describe the tradeoff between improved performance vs. increasing complexity.