Multidimensional adaptive filtering via McClellan transformations

The McClellan transformation is developed as an efficient parametrization for a least-squares (LS) adaptive filter. It is shown that the McClellan transformation is a decomposition that roughly corresponds to separating the specification of a multidimensional filter into a normal component, parameterized by the 1D prototype filter, and a tangential component, parameterized by the transformation function. Such a decomposition gives an adaptive system the potential to exploit directional biases in any direction, as opposed to separable filters, which have their symmetry constrained by the two fixed axes. Using the Chebychev recursive implementation of the McClellan transformation, it is also shown that for a given transformation function, the adaptation of the 1D prototype filter becomes a small vector-adaptation problem, similar to adaptive-array problems. For real-time LS block adaptation, such an adaptation algorithm can be performed efficiently using systolic arrays