Use of the matching pursuit algorithm with a dictionary of asymmetric waveforms in the analysis of transient evoked otoacoustic emissions

Transiently evoked otoacoustic emissions (TEOAEs) are normally modeled as the sum of asymmetric waveforms. However, some previous studies of TEOAEs used time-frequency (TF) methods to decompose the signals into symmetric waveforms. This approach was justified mainly as a means to reduce the complexity of the calculations. The present study extended the dictionary of numeric functions to incorporate asymmetric waveforms into the analysis. The necessary calculations were carried out using an adaptive approximation algorithm based on the matching pursuit (MP) numerical technique. The classic MP dictionary uses Gabor functions and consists of waveforms described by five parameters, namely, frequency, latency, time span, amplitude, and phase. In the present investigation, a sixth parameter, the degree of asymmetry, was added in order to enhance the flexibility of this approach. The effects of expanding the available functions were evaluated by means of both simulations using synthetic signals and authentic TEOAEs. The resulting analyses showed that the contributions of asymmetric components in the OAE signal are appreciable. In short, the expanded analysis method brought about important improvements in identifying TEOAE components including the correct detection of components with long decays, which are often related to spontaneous OAE activity, the elimination of a “dark energy” effect in TF distributions, and more reliable estimates of latency-frequency relationships. The latter feature is especially important for correct estimation of latency-frequency data, which is a crucial factor in investigations of OAE-generation mechanisms.