An analytic physically motivated model of the mammalian cochlea

Abstract

We develop an analytic model of the mammalian cochlea. We use a mixed physicalphenomenological approach by utilizing existing work on the physics of classical boxrepresentations of the cochlea, and behavior of recent data-derived wavenumber estimates. Spatial variation is incorporated through a single independent variable that combines space and frequency. We arrive at closed-form expressions for the organ of Corti velocity, its impedance, the pressure difference across the organ of Corti, and its wavenumber. We perform model tests using real and imaginary parts of chinchilla data from multiple locations and for multiple variables. The model also predicts impedances that are qualitatively consistent with current literature. For implementation, the model can leverage existing efforts for both filter bank and filter cascade models that target improved algorithmic or analog circuit efficiencies. The simplicity of the cochlear model, its small number of model constants, its ability to capture the variation of tuning, its closed-form expressions for physically-interrelated variables, and the form of these expressions that allows for easily determining one variable from another make the model appropriate for analytic and digital auditory filter implementations as discussed here, as well as for extracting macromechanical insights regarding how the cochlea works.

Design of FIR filters with magnitude specifications

“…In the expression, p = ib p − A p and p = −ib p − A p . The model constants A p , B u , b p take on real positive values, and we have shown that they vary slowly along the length of the cochlea [12] (recall that for many of the diverse set of applications in section I, it is desirable for the filters to mimic signal processing by the auditory system). If the filters are sharply tuned, A 2 p + b 2 p ≈ b 2 p , and if the peak frequency occurs at CF(x) (i.e.…”

“…1) Transfer functions: GAFs were derived in the frequency domain based on a physical-phenomenological model of the cochlea operating at low stimulus levels and is tightly linked to frequency domain mechanistic variables of the associated cochlear model that are useful for studying how the cochlea functions [12]. Here we extend our study of the transfer functions to rational exponent GAFs.…”

“…(3) Related filters have previously been introduced for the case of integer exponents (B u ∈ Z + ) -the All-Pole Gammatone Filters and Filterbanks (APGFs) [11], and the Generalized Auditory Filters and Filterbanks (GAFs) [12], [9]. For a subset of parameter values, these filters mimic signal processing by the auditory system.…”

“…We then introduce normalized frequency and normalized time domains in which we derive the representations, and which are useful for instances of GAF filterbanks. We present the transfer function representation (previously derived in detail in [12]) in section III and discuss the stability and causality of the rational-exponent filters. We also illustrate the continuum of behavior accessible due to relieving the integer-B u constraint.…”

“…The TF representation is ideal for testing the model against data and for estimating values of model constants from data due to the nature of much of the reported data from cochlear experiments [28]. We have demonstrated these points in previous work [12]. Additionally, the simplicity of the form of the TF representation allows us to derive parameterizations of GAFs in terms of desired or observed filter/response variable characteristics such as peak frequency, quality factor, and group delay [30].…”