The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

A unified view of algorithms for adaptive transversal FIR filtering and system identification has been presented. Wiener filtering and stochastic approximation are the origins from which all the algorithms have been derived, via a suitable choice of iterative optimization schemes and appropriate design parameters. Following this philosophy, the LMS algorithm and its offspring have been presented and interpreted as stochastic approximations of iterative deterministic steepest descent optimization schemes. On the other hand, the RLS and the quasi-RLS algorithms, like the quasi-Newton, the FNTN, and the affine projection algorithm, have been derived as stochastic approximations of iterative deterministic Newton and quasi-Newton methods. Fast implementations of these methods have been discussed. Block-adaptive, and block-exact adaptive filtering have also been considered. The performance of the adaptive algorithms has been demonstrated by computer simulations.

Efficient least squares adaptive algorithms for FIR transversal filtering

A fast, recursive least squares (RLS) adaptive nonlinear filter modeled using a second-order Volterra series expansion is presented. The structure uses the ideas of fast RLS multichannel filters, and has a computational complexity of O(N/sup 3/) multiplications, where N-1 represents the memory span in number of samples of the nonlinear system model. A theoretical performance analysis of its steady-state behaviour in both stationary and nonstationary environments is presented. The analysis shows that, when the input is zero mean and Gaussian distributed, and the adaptive filter is operating in a stationary environment, the steady-state excess mean-squared error due to the coefficient noise vector is independent of the statistics of the input signal. The results of several simulation experiments show that the filter performs well in a variety of situations. The steady-state behaviour predicted by the analysis is in very good agreement with the experimental results. >

A fast recursive least squares adaptive second order Volterra filter and its performance analysis

Recordings of diastolic heart sound segments were modeled by autoregressive (AR) methods including the adaptive recursive least-squares lattice (RLSL) and the gradient lattice predictor (GAL). Application of the Akaike criterion demonstrated that between 5 and 15 AR coefficients are required to describe a diastolic segment completely. The reflection coefficients, prediction coefficients, zeros of the polynomial of the inverse filter, and AR spectrum were determined over a number (N=20-30) of diastolic segments. Preliminary results indicate that the averaged AR spectrum and the zeros of the inverse filter polynomial can be used to distinguish between normal patients and those with coronary artery disease. >

Detection of coronary occlusions using autoregressive modeling of diastolic heart sounds

An effective method to stabilize fast RLS algorithms is proposed. It is based on the analysis of the propagation of the numerical errors according to a first-order linear model. Two variables are shown to be responsible for the numerical instability. The proposed method modifies the numerical properties of these variables, while preserving the theoretical form of the algorithms. This method is applied to the FTF (fast transversal filter) and fast Kalman algorithms. Experimental results in floating- and fixed-point arithmetic show the efficiency of the method. >

N Kalouptsidis

Papers

A unifed view of parametric processing algorithms for prewindowed signals