Direct Design of Parallel second-order filters for Instrument Body Modeling

This paper 1 presents a direct design technique for parallel second-order sections based on a perceptually motivated logarithmic scale, with application to instrument body modeling. Traditional FIR and IIR design techniques work on a linear frequency scale, which is usually not optimal for audio applications. Warped filters and Kautz filters are good candidates for perceptually motivated filter design. However, the direct implementation of warped or Kautz filters is computationally less efficient compared to an IIR filter of the same order. The perceptually motivated frequency resolution can also be achieved by the proposed design method, without the disadvantage of increased computational complexity. The filter design has two phases. First, the pole frequencies of the second-order sections are set to a predefined logarithmic scale, or can be determined from a warped filter design. Then the zeros are found by a simple least squares algorithm, as the optimization problem becomes linear in parameters for a given set of poles. As high-order (up to 1000) filters can be robustly designed, this technique is particularly well suited for instrument body modeling. Moreover, the parallel structure allows flexible modifications to the body transfer function.