Minimum mean-square-error approximation using transversal-type filters

The classical problem of weighted minimum mean-square error approximation using transversal-type filters is considered. Results from the theory of Hardy spaces are used to establish necessary and sufficient conditions for the convergence of transversal-type filters to the optimum linear causal filter. These show that the use of second-order (and higher) all-pass approximations to a pure delay is undesirable in minimum mean-square-error approximations with a weighting function which satisfies the Paley-Wiener conditions.