An Asynchronous Event-Based Algorithm for Periodic Signals

Let $0\leq\tau_{1}\leq\tau_{2}\leq\cdots\leq\tau_{m}\leq1$, originated from a uniform distribution. Let also $\epsilon,\delta\in\mathbb{R}$, and $d\in\mathbb{N}$. What is the probability of having more than $d$ adjacent $\tau_{i}$-s pairs that the distance between them is $\delta$, up to an error $\epsilon$ ? In this paper we are going to show how this untreated theoretical probabilistic problem arises naturally from the motivation of analyzing a simple asynchronous algorithm for detection of signals with a known frequency, using the novel technology of an event camera.