  We develop an analytic model of the mammalian cochlea. We use a mixed
physical-phenomenological approach by utilizing existing work on the physics of
classical box-representations 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.
