  Biomimicry is a powerful science that takes advantage of nature's remarkable
ability to devise innovative solutions to challenging problems. In this work,
we use asymptotic methods to develop the mathematical foundations for the
exchange of design inspiration and features between biological hearing systems,
signal processing algorithms and acoustic metamaterials. Our starting point is
a concise asymptotic analysis of high-contrast acoustic metamaterials. We are
able to fine tune this graded structure to mimic the biomechanical properties
of the cochlea, at the same scale. We then turn our attention to developing a
biomimetic signal processing algorithm. We use the response of the cochlea-like
metamaterial as an initial filtering layer and then add additional biomimetic
processing stages, designed to mimic the human auditory system's ability to
recognise the global properties of natural sounds. This demonstrates the
three-way exchange of ideas that, thanks to our analysis, is possible between
signal processing, metamaterials and biology.
