The time-sequenced adaptive filter

Abstract

A new form of adaptive filter is proposed which is especially suited for the estimation of a class of nonstationary signals. This new filter, called the time-sequenced adaptive filter, is an extension of the least mean-square error (LMS) adaptive filter. Both the LMS and time-sequenced adaptive filters are digital filters composed of a tapped delay line and adjustable weights, whose impulse response is controlled by an adaptive algorithm. For stationary stochastic inputs the mean-square error, which is the expected value of the squared difference between the filter output and an externally supplied "desired response," is a quadratic function of the weights-a paraboloid with a single fixed minimum point which can be sought by gradient techniques, such as the LMS algorithm. For nonstationary inputs however the minimum point, curvature, and orientation of the error surface could be changing over time. The time-sequenced adaptive filter is applicable to the estimation of that subset of nonstationary signals having a recurring (but not necessarily periodic) statistical character, e.g., recurring pulses in noise. In this case there are a finite number of different paraboloidal error surfaces, also recurring in time. The time-sequenced adaptive filter uses multiple sets of adjustable weights. At each point in time, one and only one set of weights is selected to form the filter output and to be adapted using the LMS algorithm. The index of the set of weights chosen is synchronized with the recurring statistical character of the filter input so that each set of weights is associated with a single error surface. After many adaptations of each set of weights, the minimum point of each error surface is reached resulting in an optimal time-varying filter. For this procedure, some a priori knowledge of the filter input is required to synchronize the selection of the set of weights with the recurring statistics of the filter input. For pulse-type signals, this a priori knowledge could be the location of the pulses in time; for signals with periodic statistics, knowledge of the period is sufficient. Possible applications of the time-sequenced adaptive filter include electrocardiogram enhancement and electric load prediction.