Very low sensitivity realization of IIR digital filters using a cascade of complex all-pass structures

TLDR: In this paper, a cascade of complex all-pass structures is proposed to realize recursive digital filters, which can exactly realize any elliptic transfer function, and it is easy to derive the multiplier coefficients associated with this structure from the original transfer function expression.

Abstract: A new realization of recursive digital filters based on a cascade of complex all-pass structures is proposed. The cascade realization ensures low stopband sensitivity, whereas the all-pass sections, being structurally bounded, guarantee low passband sensitivity. The proposed structure can exactly realize any elliptic transfer function, and it is easy to derive the multiplier coefficients associated with this structure from the original transfer function expression. To reduce the computational complexity, some of the coefficients are rounded to integer values and an optimum approximation to the original transfer function is obtained by using a minimax optimization procedure. Several examples show that the proposed structure requires significantly fewer bits than other known cascade-form realizations. Another advantage of the proposed structure is that it is free of overflow oscillations.