title: Analysis and design of gammatone signal models.
abstract: An established model for the signal analysis performed by the human cochlea is the overcomplete gammatone filterbank. The high correlation of this signal model with human speech and environmental sounds [E. Smith and M. Lewicki, Nature (London) 439, 978-982 (2006)], combined with the increased time-frequency resolution of sparse overcomplete signal models, makes the overcomplete gammatone signal model favorable for signal processing applications on natural sounds. In this paper a signal-theoretic analysis of overcomplete gammatone signal models using the theory of frames and performing bifrequency analyses is given. For the number of gammatone filters M> or =100 (2.4 filters per equivalent rectangular bandwidth), a near-perfect reconstruction can be achieved for the signal space of natural sounds. For signal processing applications like multi-rate coding, a signal-to-alias ratio can be used to derive decimation factors with minimal aliasing distortions.
authors.affiliation: International Graduate School for Neurosensory Science and Systems, Carl von Ossietzky University, D-26111 Oldenburg, Germany. stefan.strahl@uni-oldenburg.de
authors.forename: Stefan
authors.initials: S
authors.lastname: Strahl
authors.forename: Alfred
authors.initials: A
authors.lastname: Mertins
mesh_terms: D000162:Acoustics; D003051:Cochlea / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D010700:Phonetics; D013016:Sound; D013067:Speech Perception / Q000502:physiology*