It is sometimes required to change the frequency characteristics of a digital filter during its operation. In this paper a new synthesis of variable even-order IIR digital filters is proposed. The cut-off frequency of the filter can be changed by a single parameter. The fundamental filter structure is a cascade of second-order sections. The multiplier coefficients of each section are determined by using the Taylor series expansion of the lowpass to lowpass frequency transformation. For this method any second-order section can be used as a prototype, but here in this paper only the direct form and the lattice form are described. Unlike the conventional method, any transfer functions can be used for the proposed method. Finally a designed example shows that the proposed filter has wider tuning range than the conventional filter, and the advantage of the proposed filters is confirmed.

Low-sensitivity digital filters are required for accurate signal processing. Among many low-sensitivity digital filters, a method using complex allpass circuits is well-known. In this paper, a new synthesis of complex allpass circuits is proposed. The proposed synthesis can be realized more easily either only in the z-domain or in the s-domain than conventional methods. The key concept for the synthesis is based on the factorization of lossless scattering matrices. Complex allpass circuits are interpreted as lossless digital two-port circuits, whose scattering matrices are factored. Furthermore, in the cases of Butterworth, Chebyshev and inverse Chebyshev responses, the explicit formulae for multiplier coefficients are derived, which enable us to synthesize the objective circuits directly from the specifications in the s-domain. Finally design examples verify the effectiveness of the proposed method.

It is often desired to change the cutoff frequencies of digital filters in some applications like digital electronic instruments. This paper proposes a design of variable lowpass digital filters with wider ranges of cutoff frequencies than conventional designs. Wave digital filters are used for the prototypes of variable filters. The proposed design is based on the frequency scaling in the s-domain, while the conventional ones are based on the z-domain lowpass-to-lowpass transformations. The first-order approximation by the Taylor series expansion is used to make multiplier coefficients in a wave digital filters obtained from a frequency-scaled LC filter become linear functions of the scaling parameter, which is similar to the conventional design. Furthermore this paper discusses the reduction of the approximation error. The curvature is introduced as the figure of the quality of the first-order approximation. The use of the second-order approximation to large-curvature multiplier coefficients instead of the first-order one is proposed.