The authors introduce a family of rapidly converging IIR (infinite impulse response) adaptive algorithms with O(N) computational complexity, where N is the filter order. By observing the similarity between the numerical solution of partial differential equations and the IIR adaptive filtering problem, results from the solution of systems of sparse linear equations may be employed. In this formulation the identification problem of the IIR coefficients separates into two subproblems, each of which may be solved by application of fast adaptive FIR (finite impulse response) techniques. Present IIR algorithms require greater computational cost or converge more slowly.
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