New Levinson, Schur, and lattice type algorithms for linear phase filtering

The LS estimate of the impulse response of FIR filters with linear phase is known to be given by a structured linear set of equations. Three new algorithms are presented for the efficient solution of such systems. One is the unwindowed extension of a previously derived Levinson-type structurally symmetric algorithm. The second is a novel exact least squares lattice algorithm for time-recursive processing. The third is a Schur-type structurally symmetric algorithm with high degree of parallelism. The new structures have considerably lower computational complexity and more parsimonious parametrization compared to previously derived algorithms. This is because, in contrast to the previously derived algorithms, the new algorithms are developed so as to respect the symmetry which is intrinsic in the linear phase problem