Causality-constrained measurements of aural acoustic reflectance and reflection functions

Causality-constrained procedures are described to measure acoustic pressure reflectance and reflection function (RF) in the ear canal or unknown waveguide, in which reflectance is the Fourier transform of the RF. Reflectance calibration is reformulated to generate causal outputs, with results described for a calibration based on a reflectance waveguide equation to calculate incident pressure and source reflectance in the frequency domain or source RF in the time domain. The viscothermal model RF of each tube is band-limited to the stimulus bandwidth. Results are described in which incident pressure is either known from long-tube measurements or calculated as a calibration output. Calibrations based on constrained nonlinear optimizations are simpler and more accurate when incident pressure is known. Outputs measured by causality-constrained procedures differ at higher frequencies from those using standard procedures with non-causal outputs. Evanescent-mode effects formulated in the time domain and incorporated into frequency-domain calibrations are negligible for long-tube calibrations. Causal reflectance and RFs are evaluated in an adult ear canal and time- and frequency-domain results are contrasted using forward and inverse Fourier transforms. These results contribute to the long-term goals of improving applications to calibrate sound stimuli in the ear canal at high frequencies and diagnose conductive hearing impairments.