Multi-scale event detection and period extraction

We describe a system for detecting complex discrete periodic events by identifying symmetries in their scale-space representation using a medial-axis transform. Whilst allowing events with varying characteristics and very low signal to noise ratios to be detected, this also has the potential to introduce a large number of false alarms. We, therefore, also present an entropy-based algorithm that can robustly extract periodicities from a set of observed events with a large proportion of missing or false alarms. The problem of detecting discrete periodic signals and extracting their characteristics is frequently encountered in communications, radar and speech processing applications. The event detection and period extraction processes described here have a low computational cost and can extract signal periodicity after a short observation time (less that 10 repetitions of the period). We demonstrate a period extraction algorithm that is faster than previously reported algorithms and more robust than many, including those based on histogramming and Kalman filtering. When the number of false alarms equals that of detected events the period is correctly determined in 90% of cases (compared to 40% for a Fourier based algorithm). A technique using circular statistics gives 95% success but requires 10 times more computation.