Investigating routes to chaos in the guinea-pig cochlea using the continuous wavelet transform and the short-time Fourier transform

The continuous wavelet transform (CWT) and the short-time Fourier transform (STFT) were used to analyze the time course of cellular motion in the guinea pig inner ear. The velocity responses of individual outer hair cells and Hensen's cells to amplitude modulated (AM) acoustical signals applied to the ear canal displayed characteristics typical of nonlinear systems, such as the generation of spectral components at harmonics of the carrier frequency. Nonlinear effects were particularly pronounced at the highest stimulus levels, where half-harmonic (and sometimes quarter-harmonic) components were also seen. The generation of these components was consistent with the behavior of a dynamical system entering chaos via a period-doubling route. A negative-stiffness Duffing oscillator model yielded period-doubling behavior similar to that of the experimental data. We compared the effectiveness of the CWT and the STFT for analyzing the responses to AM stimuli. The CWT (calculated using a high-Q Morlet-wavelet basis) and the STFT were both useful for identifying the various spectral components present in the AM velocity response of the cell. The high-Q Morlet wavelet CWT was particularly effective in distinguishing the lowest frequency components present in the response, since its frequency resolution is appreciably better than the STFT at low frequencies. Octave-band-based CWTs (using low-Q Morlet, Meyer, and Daubechies 4-tap wavelets) were largely ineffective in analyzing these signals, inasmuch as the frequency spacing between neighboring spectral components was far less than one octave.