Design of FIR/IIR lattice filters using the circulant matrix factorization

Abstract

We propose the methods to design the finite impulse response (FIR) and the infinite impulse response (IIR) lattice filters using Schur's (1917) algorithm through the spectral factorization of the covariance matrix by circulant matrix factorization. Circulant matrix factorization is also very powerful tool used for spectral factorization of the covariance polynomial in matrix domain to obtain the minimum phase polynomial without the polynomial root finding problem. The Schur algorithm is a method for fast Cholesky factorization of the Toeplitz matrix, which easily determines the lattice filter parameters. Examples for the case of the FIR filter and for the IIR filter are included, and the performance of our method is checked by comparison with other methods (polynomial root finding and cepstral deconvolution).