Synthesis of complex allpass circuits using the factorization of scattering matrices - explicit formulae for even-order real complementary filters having Butterworth or Chebyshev responses

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 formulate 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.