Introducing causality violation for improved DPOAE component unmixing

The DPOAE response consists of the linear superposition of two components, a nonlinear distortion component generated in the overlap region, and a reflection component generated by roughness in the DP resonant region. Due to approximate scaling symmetry, the DPOAE distortion component has approximately constant phase. As the reflection component may be considered as a SFOAE generated by the forward DP traveling wave, it has rapidly rotating phase, relative to that of its source, which is also equal to the phase of the DPOAE distortion component. This different phase behavior permits effective separation of the DPOAE components (unmixing), using time-domain or time-frequency domain filtering. Departures from scaling symmetry imply fluctuations around zero delay of the distortion component, which may seriously jeopardize the accuracy of these filtering techniques. The differential phase-gradient delay of the reflection component obeys causality requirements, i.e., the delay is positive only, and the fine-structure oscillations of amplitude and phase are correlated to each other, as happens for TEOAEs and SFOAEs relative to their stimulus phase. Performing the inverse Fourier (or wavelet) transform of a modified DPOAE complex spectrum, in which a constant phase function is substituted for the measured one, the time (or time-frequency) distribution shows a peak at (exactly) zero delay and long-latency specular symmetric components, with a modified (positive and negative) delay, which is that relative to that of the distortion component in the original response.