Introducing the Differentiated All-Pole and One-Zero Gammatone Filter Responses and their Analogue VLSI Log-domain Implementation

Abstract—The scope of this paper is to introduce two particu-lar filter responses which closely resemble tuning curves at specific set of places on the basilar membrane (BM) of the bio-logical cochlea. The responses are termed Differentiated All-Pole Gammatone Filter (DAPGF) and One-Zero Gammatone Filter (OZGF) and their form suggest their implementation by means of cascades of N identical two-pole systems, which makes them excellent candidates for efficient analog VLSI implementations. The resulting filters can be used in a filter-bank architecture to realize cochlea implants or auditory proc-essors of increased biorealism. In addition, their simple parameterization allows the use of conventional automatic gain control (AGC) schemes to model certain important features of the biological cochlea (e.g. level-dependent gain) that are ob-served physiologically. To illustrate the idea, we present pre-liminary simulation results from a 4th-order OZGF using novel high dynamic range log-domain biquads in CMOS weak inver-sion (CMOS-WI). All circuits were designed in Cadence® Design Framework, using the commercially available AMS 0.35µm CMOS process. The reported OZGF structure has a simulated input dynamic range of 114.5dB, while dissipating 3.7µW of static power. I