Implementing the Fourier transform in a sensor: a benchmark application for neuromorphic acoustic sensing

Abstract In changing environments, the mammalian hearing perception so far outperforms technical speech processing. This is enabled by the nonlinear dynamics of the cochlea. Inside of it, the processing is based on a frequency decomposition and a sophisticated feedback loop, so that the amplification of spectrum of an external signal can vary from linear to compressive. This behavior can be mimicked by implementing a controllable Andronov–Hopf bifurcation into neuromorphic oscillators, which enables a compressive and frequency-selective response. However, the frequency decomposition with these neuromorphic oscillators has not been investigated yet. Here, we show that any oscillator, which exhibits an Andronov–Hopf bifurcation, has a unique response to external stimuli, if its bifurcation parameter is in a neighborhood of the critical point. In addition, we propose three different algorithms to enable the frequency decomposition by implementing the Fourier transform in an acoustic sensor. We found that this Fourier transform can be done by applying amplitude demodulation to the output of any oscillator exhibiting at least one Andronov–Hopf bifurcation and investigated the convergence time of the different algorithms. Our results demonstrate that the Fourier transform can be utilized for either a single oscillator, which is simple to implement, or an array of oscillators, which has a fast convergence time. Thereby, it is shown that the neuromorphic acoustic sensor consisting of these oscillators can both mimic the processing of the cochlea and be implemented into the technical unit. Finally, a potential experimental implementation using micro-electromechanical system sensors is proposed.