An echolocation model for the restoration of an acoustic image from a single-emission echo

Bats can form a fine acoustic image of an object using frequency-modulated echolocation sound. The acoustic image is an impulse response, known as a reflected-intensity distribution, which is composed of amplitude and phase spectra over a range of frequencies. However, bats detect only the amplitude spectrum due to the low-time resolution of their peripheral auditory system, and the frequency range of emission is restricted. It is therefore necessary to restore the acoustic image from limited information. The amplitude spectrum varies with the changes in the configuration of the reflected-intensity distribution, while the phase spectrum varies with the changes in its configuration and location. Here, by introducing some reasonable constraints, a method is proposed for restoring an acoustic image from the echo. The configuration is extrapolated from the amplitude spectrum of the restricted frequency range by using the continuity condition of the amplitude spectrum at the minimum frequency of the emission and the minimum phase condition. The determination of the location requires extracting the amplitude spectra, which vary with its location. For this purpose, the Gaussian chirplets with a carrier frequency compatible with bat emission sweep rates were used. The location is estimated from the temporal changes of the amplitude spectra.