Linear transformations for the design of digital and active filters

In this paper, new structures are proposed for the realization of two-dimensional (2-D) stable recursive filters. Such structures are derived from 1-D analog doubly-terminated LC ladder networks by first creating a suitable 2-D analog ladder structure using the method outlined in (1), and then utilizing the linear transformation technique to derive the corresponding 2-D structures. In doing so, the resulting structures are not only ensured to be recursively stable, but they also enjoy very low sensitivity to variations in multiplier coefficient values, and their round-off noise is expected to be low. The technique of linear transformations is applied to the design of low sensitivity active filter structures, and one particular scheme leading to an economical realization is outlined. Examples are included to illustrate the excellent low sensitivity of the derived structures.