Eigen-approach for designing FIR filters and all-pass phase equalizers with prescribed magnitude and phase response

An effective eigenfilter approach is proposed for designing FIR filters with complex-valued frequency responses. By minimizing a quadratic measure of the error in the frequency band, an eigenvector of an appropriate matrix is computed to get the filter coefficients. The algorithm is easy and optimal in the least squares sense; it is used to design to major classes of FIR filters, including multiband filters, differentiators, Hilbert transformers, and all-pass phase. Several examples and comparisons to the existing linear programming methods are presented to demonstrate the flexibility and effectiveness of this approach