The eigenfilter for the design of linear-phase filters with arbitrary magnitude response

The author studies the design of linear-phase FIR (finite impulse response) digital filters to approximate linear-phase functions with arbitrary magnitude response. The design method is based on the computation of an eigenvector of an appropriate real, symmetric, and positive-definite matrix. The design of complex-coefficient linear-phase filters is shown to be an extension of the design of the real-coefficient filter. Several examples are presented which demonstrate the usefulness of the approach.<>