This paper introduces a new adaptive filtering algorithm called fast affine projections (FAP). Its main attributes include RLS (recursive least squares) like convergence and tracking with NLMS (normalized least mean squares) like complexity. This mix of complexity and performance is similar to the recently introduced fast Newton transversal filter (FNTF) algorithm. While FAP shares some similar properties with FNTF it is derived from a different perspective, namely the generalization of the affine projection interpretation of NLMS. FAP relies on a sliding windowed fast RLS (FRLS) algorithm to generate forward and backward prediction vectors and expected prediction error energies. Since sliding windowed FRLS algorithms easily incorporate regularization of the implicit inverse of the covariance matrix, FAP is regularized as well.

Meeting Name

IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 1993


Electrical and Computer Engineering

Keywords and Phrases

Adaptive Filters; Affine Projection Interpretation; Backward Prediction Vectors; Convergence of Numerical Methods; Covariance Matrices; Covariance Matrix; Echo Cancellation; Echo Suppression; Fast Newton Transversal Filter Algorithm; Fast Affine Projections; Forward Prediction Vectors; Least Mean Squares Methods; Low Complexity Adaptive Filtering Algorithm; Normalized Least Mean Squares Like Complexity; Performance; Prediction Error Energies; Recursive Filters; Recursive Least Squares Like Convergence; Regularization; Sliding Windowed Fast RLS Algorithm; Tracking

Document Type

Article - Conference proceedings

Document Version

Final Version

File Type





© 1993 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jan 1993