24 - A continuous time approach to the analysis and design of parallel algorithms for subspace tracking

Abstract

Continuous time equivalents of discrete time algorithms are often surprisingly simple, and allow for easy manipulation, analysis and parallelization. Moreover, they establish a connection between systolic arrays and adaptive neural networks. Up to now, the connection between discrete and continuous time algorithms for adaptive signal processing has been established mainly through Ljungs approach, using differential equations parametrized by an input correlation matrix, for the asymptotic analysis of iterative algorithms. The approach in this chapter works with a continuous time input, and uses exact integration for the case of a piecewise-constant input signal to establish the connection with discrete time algorithms.