Many animal species are known for their unparalleled abilities to encode sensory information that supports fast, reliable action in complex environments, but the mechanisms remain often unclear. Through fast ear motions, bats can encode information on target direction into time-frequency Doppler signatures. These species were thought to be evolutionarily tuned to Doppler shifts generated by a prey's wing beat. Self-generated Doppler shifts from the bat's own flight motion were for the most part considered a nuisance that the bats compensate for. My findings indicate that these Doppler-based biosonar systems may be more complicated than previously thought because the animals can actively inject Doppler shifts into their input signals. The work in this dissertation presents a novel nonlinear principle for sensory information encoding in bats. Up to now, sound-direction finding has required either multiple signal frequencies or multiple pressure receivers. Inspired by bat species that add Doppler shifts to their biosonar echoes through fast ear motions, I present a source-direction finding paradigm based on a single frequency and a single pressure receiver. Non-rigid ear motions produce complex Doppler signatures that depend on source direction but are difficult to interpret. To demonstrate that deep learning can solve this problem, I have combined a soft-robotic microphone baffle that mimics a deforming bat ear with a CNN for regression. With this integrated cyber-physical setup, I have able to achieve a direction-finding accuracy of 1 degree based on a single baffle motion.