Digital filter synthesis by sampled-data transformation

The design of digital filter transfer functions is facilitated by taking advantage of well-established design techniques developed for continuous (analog) filters. Digital approximations to continuous filter functions may be found by applying an appropriate sampled-data (z) transformation to the continuous filter transfer function. Three mathematical transformations are described that find the most application: 1) the standard z-transform, 2) the bilinear z-transform, and 3) the matched z-transform. The applicability of the three transformations is discussed and examples are presented of digital filters designed using these transformations.