Models for approximating basilar membrane displacement

Three analytical models are developed for estimating the displacement of the basilar membrane in the human ear when the sound pressure at the eardrum is known. Frequency-domain data, derived experimentally by Bekesy, are Fourier-transformed to examine the impulse response of the membrane. Time-domain and frequency-domain responses of the models are compared with the experimental data. Excitation of the models by periodic impulses is considered. Calculations of membrane displacement are made for excitation by positive pulses, and by alternately positive and negative pulses. Applicability of the results to the perception of pitch is indicated.