Explicit Expression for a Linear Filter in Terms of Its Lattice Representation

A causal digital autoregressive filter is completely defined by a polynomial P. In the general case, and particularly for stable filters, it is well-known that P can be expressed recursively in terms of the so-called reflection coefficients k
_j
appearing in the lattice representation of the associated filter. This letter proposes an explicit expression for polynomial P in terms of the coefficients kj
_.