Design of low-sensitivity digital filters by linear transformations

In this paper, the linear transformation approach to the design of digital filter structures from analog doubly terminated lossless ladder filters is investigated. It is shown that there exist several families of linear transformations which all produce different realization schemes for digital filter structures that possess low sensitivity to variations in multiplier coefficients, the "wave digital filters" and those discussed in [1], [2] being special cases of a more general transformation set. Such structures are expected to behave differently as far as roundoff noise, dynamic range, and limit cycles are concerned. By a judicious choice of the transformation matrices and their cycle length, new structures with extremely high modularity and with lower complexity than many of the hitherto known methods are derived. Finally, it is shown that stringent attenuation specifications can successfully be met with digital structures that include no actual multipliers, but merely simple shift operations, thus demonstrating the excellent low sensitivity of these structures.