Circular lattice filtering using Pagano's method

Recently, Pagano has found a one-to-one relationship between multivariate autoregression and scalar periodic autoregressions, and derived a set of fundamental Yule-Walker (YW) type equations for estimating the parameters of the periodic autoregressions. In this paper, we first obtain a Levinson-type recursive algorithm for solving the above mentioned YW equations. Then using this recursion we show a circular lattice structure of the process. This enables us to obtain a Burg-type algorithm which guarantees the filter stability. Lastly, we modify it to an adaptive form for on-line computation. This circular lattice filter simultaneously performs whitening and orthogonalization of the components of multivariate input samples. The most salient feature of the algorithm is that it consists of calculations of scalar quantities, thus completely avoiding matrix manipulations accompanying usual multivariate processing methods.