Quadrature mirror filter design in the time domain

TLDR: In this article, a new technique for designing quadrature mirror filters is described, which is carried out in the time domain and results in an optimization problem requiring minimization of a quartic multinomial.

Abstract: A new technique for designing quadrature mirror filters is described. The formulation, carried out in the time domain, is shown to result in an optimization problem requiring minimization of a quartic multinomial. An iterative solution is suggested which involves (computation of) the eigenvector of a matrix with a dimensionality equal to one half the number of filter taps. Our experiments show that convergence to the optimum tap weights is stable, and the accuracy of the final solution is limited only by the accuracy of the eigenvalue-eigenvector routine. As in an earlier technique, the user can specify the stop: band frequency the relative weights of the passband ripple energy and the stopband residual energy, and, of course, the number of filter taps.