A modified normalized lattice adaptive filter for fast sampling

Most filters, adaptive or not, formulated using the delay operator, have no limit when sampling becomes fast and therefore they will have numerical problems. We will show that one reason that the normalized lattice filter has less numerical problems is because that it has a limit as the sampling period tends to zero. The transfer function in the s-domain obtained as a limit of the normalized lattice filter will, however, have only every other power in the denominator polynomial. We propose a modified normalized lattice filter that can realize any arbitrary transfer function in the discrete (z) domain and its order-recursive limit, as the sampling period tends to zero, can realize any arbitrary transfer function in the s-domain. Various stability properties of the new lattice are also studied