Optimal Scale-Invariant Wavelet Representation and Filtering of Human Otoacoustic Emissions

Otoacoustic emissions (OAEs) are generated in the cochlea and recorded in the ear canal either as a time domain waveform or as a collection of complex responses to tones in the frequency domain (Probst et al. J Account Soc Am 89:2027-2067, 1991). They are typically represented either in their original acquisition domain or in its Fourier-conjugated domain. Round-trip excursions to the conjugated domain are often used to perform filtering operations in the computationally simplest way, exploiting the convolution theorem. OAE signals consist of the superposition of backward waves generated in different cochlear regions by different generation mechanisms, over a wide frequency range. The cochlear scaling symmetry (cochlear physics is the same at all frequency scales), which approximately holds in the human cochlea, leaves its fingerprints in the mathematical properties of OAE signals. According to a generally accepted taxonomy (Sher and Guinan Jr, J Acoust Soc Am 105:782-798, 1999), OAEs are generated either by wave-fixed sources, moving with frequency according with the cochlear scaling (as in nonlinear distortion) or by place-fixed sources (as in coherent reflection by roughness). If scaling symmetry holds, the two generation mechanisms yield OAEs with different phase gradient delay: almost null for wave-fixed sources, and long (and scaling as 1/f) for place-fixed sources. Thus, the most effective representation of OAE signals is often that respecting the cochlear scale-invariance, such as the time-frequency domain representation provided by the wavelet transform. In the time-frequency domain, the elaborate spectra or waveforms yielded by the superposition of OAE components from different generation mechanisms assume a much clearer 2-D pattern, with each component localized in a specific and predictable region. The wavelet representation of OAE signals is optimal both for visualization purposes and for designing filters that effectively separate different OAE components, improving both the specificity and the sensitivity of OAE-based applications. Indeed, different OAE components have different physiological meanings, and filtering dramatically improves the signal-to-noise ratio.