ABSTRACT
This chapter discusses the development of the adaptive filter is the fixed least-squares operator given by equations. The least-squares technique provides a powerful approach to digital filtering in situations where a fixed, finite length filter is applicable. Indeed, this approach has achieved widespread application in many areas. The principal problem arises when the input data is statistically non-stationary. Although the normal equations can be formulated for non-stationary inputs, the calculation of the non-stationary correlation coefficients presents difficulties. A different least-squares operator is then computed for each optimization interval. This technique of subdividing a piece of data into smaller intervals referred to as windows or gates, over which the signal is considered stationary, is widespread in speech and seismic processing among other applications. The chapter presents the general components of an adaptive filter; these comprise three essential elements: the structure of the filter, the overall system configuration and performance criterion for adaptation.
