Lossy synthesis of digital lattice filters

A new method fur converting a lossless cascade lattice realization of a real, stable, single-input, single-output (ARMAn, n) filter, with a lossy constant terminating one-port section, to a lossy realization is proposed. The conversion process is carried out through the factorization of the transfer scattering matrix of a two-port equivalent of the terminating section and the distribution of the loss term, embedded in this matrix, among the lossless lattice sections according to some desirable pattern. The cascade is then made computable through the extraction of right-matched I-unitary normalization sections. The technique applies to both degree-one and degree-two lattice sections, and is rendered systematic owing to the particular lossless lattice structure used. The motivation for this work lies in the synthesis of a pipeline of digital cochlea lattices with loss suitable for hearing impairment diagnosis via Kemp echoes.