Analysis and design of gammatone signal models

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.