Event-Driven Prony: Towards Asynchronous Spectral Estimation

Mainstream signal processing theory and methods are primarily designed for synchronous sampling architectures, where samples are captured at predefined time instants. While this fits well with Shannon’s framework, in the absence of synchronous structure, even fundamental tools like filtering and convolution break down. Alternatively, event-driven or time-encoded sampling offers a more efficient method by capturing signals only when an event occurs. This approach, reminiscent of the "spiking neuron" behavior in the brain, can lead to low-power electronic implementations. Unlike Shannon’s framework, measurements in this scheme are defined by asynchronous sampling, presenting unique challenges. One such open problem is performing spectral estimation from asynchronous samples. In this paper, we propose a novel approach that directly enables spectral estimation from asynchronous measurements. Empirically, our algorithm offers robust, high-resolution spectral information, with a lower sampling rate on trigger times. Beyond numerical experiments, we build an event-driven sampling hardware utilizing asynchronous sigma-delta modulators to validate our approach. These hardware experiments further demonstrate the robustness and practical applicability of our method.