Nonlinear All-Pole and One-Zero Gammatone Filters

Martin Pflüger, Robert Höldrich, Willibald Riedler

Summary
A nonlinear model of auditory filtering in the digital domains is proposed. It is given in a general form, because of a missing quantitative description of how output level dependent auditory filter shapes change with level and frequency. The nonlinear filter is derived from an 8th order linear gammatone filter consisting of 4 biquad sections with identical pole positions [1]. The order of the nonlinear filter is constant. The low frequency branch of the filter rises with increasing control levels. The filter center frequency is approximately level independent. The impulse response becomes shorter with increasing levels. The control level of the general model is split into six level dependent control parameters which control three pole pair positions. These control parameters are adapted to the auditory filter shapes reported in Rosen and Baker [2] and the resulting magnitude responses are found to provide an excellent fit. For the given example, the control structure of the general model can be simplified by reducing the number of level dependent control parameters to two. In view of a nonlinear auditory filterbank, a frequency transposition of a single prototype filter is proposed. Therefore, it is possible to adapt the simplified control to any filter center frequency.

published in: Acustica, acta acustica Vol. 83 1997, p. 513 - 519