Invariance principles for cochlear mechanics: Hearing phases

A functional model of the cochlea is devised on the basis of the results from classical experiments. The basilar membrane filter is investigated in detail. Its phase is close to linear in the region around the peak of the amplification. On one side this has consequences for the time analysis and on the other side this has led to a prediction on phase perception for very simple combinations of tones, a prediction which is now confirmed by experiments. Equivariance under the dilation group permits one to describe the model by a wavelet transform [ Daubechies , Ten Lectures on Wavelets ( SIAM , Philadelphia, 1992 ) ]. The wavelet is discussed in reference to the phase analysis of the basilar membrane filter.