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It has been previously shown that a real-time decomposition of the incoming signal into a set of partially uncorrelated components via an orthogonal transform, and a subsequent adaptation on these individual components, leads to faster convergence rates. Here, transform domain processing is characterized by the effect of the transform on the shape of the mean-square error surface. It is shown that the effect of an ideal transform is to convert equal error contours that are initially hyperellipses in the parameter space into hyperspheres. Five specific real-valued orthogonal transforms are compared in terms of learning characteristics and computational complexity. Since the Karhunen-Loeve transform (KLT) is the ideal transform for this application, and since the KLT is defined in terms of the statistics of the input signal, it is certain that no fixed-parameter transform can deliver optimal learning characteristics for all input signals. However, the simulations suggest that transforms can be found which give much improved performance in a given situation. > |
