Two-layer Linear Structures for Fast Adaptive Filtering

Two-Layer Linear Structures for Fast Adaptive Filtering Fran coise Beaufays, Bernard Widrow Abstract The LMS algorithm invented by Widrow and Ho in 1959 is the simplest, most robust, and one of the most widely used algorithms for adaptive ltering. Unfortunately, it su ers from high sensitivity to the conditioning of its input autocorrelation matrix: the higher the input eigenvalue spread, the slower the convergence of the adaptive weights. This problem can be overcome by preprocessing the inputs to the LMS lter with a xed data-independent transformation that, at least partially, decorrelates the inputs. Typically, the preprocessing consists of a DFT or a DCT transformation followed by a power normalization stage. The resulting algorithms are called DFT-LMS and DCT-LMS. A fast and robust implementation of the DFT or the DCT preprocessing stage is itself obtained by using an adaptive lter based on the LMS algorithm. The overall structure is thus a fully adaptive two-layer linear lter, which achieves better speed performance than pure LMS while retaining its low computational cost and its extreme robustness. Introduction z -1 Input Signal

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