Filter Design Using Transformed Variables

A concise description is given of some recently developed filter design techniques. The discussion includes equal-ripple and maximally flat passband filters with general stopbands, as well as equal-ripple stopband filters with general passbands. To solve the approximation problem and to improve numerical conditioning, the design is carried out exclusively in terms of one or two transformed frequency variables. A step-by-step description is given for the design of each filter type; the steps are so formulated that the erosion of significant digits is minimized. The design processes given are unique and are directly suitable for automatic computer programs. Experience with such programs, using the algorithms described in the paper, indicates that filters up to about degree 30 may be designed using only single precision in the calculations. A discussion of some practical predistortion techniques, as well as a listing of available tabulated filter design information, is also included.