Joint parameter optimization of differentiated discretization schemes for audio circuits

We propose a new approach to discretizing audio circuits which involves applying differentiated discretization schemes among the elements of a linear circuit, or sub-circuit, rather than a single uniform scheme. The scheme coefficients are jointly optimized to minimize some frequency response error function for that linear circuit. We describe the mathematical framework for this optimization and apply it to the case of the parametric bilinear transform. Differentiated discretization coefficients are jointly optimized by minimizing the L2-norm error between the discretized frequency response and the frequency response of the original system. To demonstrate the validity of our approach, we apply our method to several examples and show a systematic reduction of the frequency response error in each case.