Stable lattice filters and their continuous-time limits

In this paper, we study some well-known lattice filters in terms of their limiting behavior as the sampling rate increases. With a fixed number of stages, the lattice structures will have an order-recursive continuous-time limit with a finite number of discrete stages, as opposed to some previous work with an infinite number of continuous stages as the limit. We study a scaled version of the two-multiplier lattice filter and the normalized lattice filter, and will show that they have continuous-time limits as the sampling period approaches zero. These limits, however, can only realize continuous-time transfer functions with every other order. A modification is proposed and is seen to have a continuous-time limit which can realize any all-pole transfer function. Stability of these filters is studied in both the discrete-time and the limiting continuous-time structures. We also investigate in detail both time-invariant as well as time-varying stability. Numerical examples show that the modified normalized lattice filter is much better behaved than the conventional normalized lattice filter under fast sampling and finite precision implementation.