Acoustic computational metamaterials for dispersion Fourier transform in time domain

Abstract

Acoustic computational metamaterials have enabled the realization of mathematical operations in the spatial domain. Here, we design acoustic computational metamaterials for performing a dispersion Fourier transform in a real-time domain. We proceed with our design using a "U" shape runway acoustic tube metamaterial with an almost linear group delay and flat amplitude with respect to acoustic frequency at around 4.45 kHz. We demonstrate our design by testing the real-time performance of three different types of pulse responses of the metamaterial, compared to the exact solutions of the Fourier transform of input signals. The simulated output results show a good fit to the exact solutions. We expect that acoustic computational metamaterials will enable new capabilities in signal acquisition and processing, network computing, and drive new applications of sound waves.