Digital implementation of linear gammatone filters: Comparison of design methods

Abstract

Digital implementations of linear gammatone filters are regularly part of auditory models and can be used in the sound processing in cochlear implants. How close digital impulse, magnitude, and phase responses match the corresponding properties of the analog gammatone filter is evaluated for one, finite-impulse response filter design, and for five, infinite-impulse response filter designs: base-band impulse invariant transformation, impulse invariant transformation, matched z transformation, bilinear transformation, and mapping of differentials with backward differences. Filter properties and computational cost are compared as a function of the filter’s order and center frequency, and sampling frequency. Results show that filters designed with the base-band impulse invariant transformation give the best overall approximation of the analog properties with reasonable computational cost.