A numerical approach to the synthesis of recursive phase equalizers

An algorithm is proposed for designing multidimensional recursive phase equalizers. In this technique, the multidimensional filter which has the prescribed amplitude response is cascaded with an equalizer to meet the required phase characteristic. The equalizer coefficients are computed by using an modified version of the Rosenbrock pattern search method. This powerful numerical method does not require the computation of derivatives, which in turn reduces the intensity of computations considerably. For stability analysis, the proposed algorithm uses the De Carlo-Strintzis theorem, which reduces an m-dimensional stability test procedure to m one-dimensional stability tests and consequently reduces the computational intensity of the algorithm in higher dimensions. To illustrate the proposed algorithm, examples for designing two-dimensional equalizers are included