Finding the poles of the lattice filter

The lattice filter is often used in spectral analysis problems. Once the reflection coefficients
{c_{k}}
are found, the task remains of extracting spectral information from them. Frequently this is done by DFT methods. An appealing alternative is to find the poles (modes) of the lattice directly. In this paper, we present an algorithm for computing the poles of the lattice directly from the
{c_{k}}
. The algorithm is based on the continued fraction expansion representation for the transfer function of the lattice. When applied to a sinusoid in noise, the algorithm found the poles, and hence the sinusoid's frequency, in less time than it took using a DFT-based peak detector. Another efficient algorithm is presented which computes the number of poles lying outside the unit circle. It is also based on information obtained directly from the
{c_{k}}
and employs only integer addition. Finally, it is shown that, by an adaptation of this algorithm, the number of poles lying in an annulus
R < |z| < 1
can be determined.