DESIGN OF DIGITAL ALLPASS NETWORKS BASED ON THE EIGENVALUE PROBLEM

This paper presents a new method of the phase design for the digital a llpass network utilizing the eigenvalue problem. The proposed design m ethod considers the phase error between the phase response of the allp ass network to be realized and the ideal phase response. The design pr oblem is formulated as an eigenvalue problem based on the Remez algori thm. By calculating the eigenvector corresponding to the maximum eigen value, the filter coefficients are determined and the optimal approxim ate solution is obtained by iterative calculation. In the design metho d, the eigenvector corresponding to the maximum eigenvalue is calculat ed to determine the filter coefficients so that the phase error is min imized. Consequently, the convergence of the design algorithm is guara nteed. Usually, the optimal approximate solution is obtained by severa l times of iterations. The error-ratio of the phase characteristics ca n be set arbitrarily, and the stability of the filter is ensured. Fina lly, the method is extended to the phase design for the digital allpas s network with complex coefficients, several design examples are shown , and the usefulness of the proposed design method is demonstrated.