Stable lattice filters and their continuous-time limits

In this paper, are study some well-known lattice filters in terms of their limiting behavior as the sampling rate increases. With a fixed number of st ages, the lattice structures will hare an order-recursive continuous-time l imit with a finite number of discrete stages, as opposed to some previous w ork with an infinite number of continuous stages as the limit. We study a s caled version of the two-multiplier lattice filter and the normalized latti ce filter, and will show that they have continuous-time limits as the sampl ing period approaches zero. These limits, however, can only realize continu ous-time transfer functions with every other order. A modification is propo sed and is seen to have a continuous-time limit which can realize any all-p ole transfer function. Stability Of these filters is studied in both the di screte-time and the limiting continuous-time structures. We also investigat e in detail both time-invariant as well as time-varying stability. Numerica l examples show that the modified normalized lattice fitter is much better behaved than the conventional normalized lattice filter under fast sampling and finite precision implementation.