On Neuromorphic Signal Pre-Processing: Enabling Sampling in the Frequency Domain with an Adaptive Frequency Controller

Signal pre-processing in the mammalian cochlea is done by a sophisticated feedback loop, where the external stimuli is decomposed into its frequency components and is nonlinearly amplified. To mimic this pre-processing, frequency-selective oscillators, whose characteristic frequency can be adjusted by a controllable input, can be utilized. With this, sampling in the frequency domain is enabled. However, it is often difficult to determine the precise analytic relationship between the input and the characteristic frequency. To this end, the work proposes an adaptive frequency controller is proposed for an Andronov-Hopf oscillator to adjust its characteristic frequency without knowing the parameters of this relationship. For this, it is shown that an Andronov-Hopf oscillator has an unique and asymptotically stable response. By asserting a desired frequency in the harmonic excitation, an adaptive controller is designed that stabilizes the characteristic frequency in a neighborhood of the desired frequency.