Detection, Measurement and Classification of Discontinuities of Signals Captured with Noise

Abstract

In this work, we propose an algorithm for the detection, measurement and classification of discontinuities in signals captured with noise. Our approach is based on the Harten’s subcell-resolution approximation adapted to the presence of noise. This technique has several advantages over other algorithms. The first is that there is a theory that allows us to ensure that discontinuities will be detected as long as we choose a sufficiently small discretization parameter size. The second is that we can consider different types of discretizations such as point values or cell-averages. In this work, we will consider the latter, as it is better adapted to functions with small oscillations, such as those caused by noise, and also allows us to find not only the discontinuities of the function, jumps in functions or edges in images, but also those of the derivative, corners. This also constitutes an advantage over classical procedures that only focus on jumps or edges. We present an application related to heart rate measurements used in sport as a physical indicator. With our algorithm, we are able to identify the different phases of exercise (rest, activation, effort and recovery) based on heart rate measurements. This information can be used to determine the rotation timing of players during a game, identifying when they are in a rest phase. Moreover, over time, we can obtain information to monitor the athlete’s physical progression based on the slope size between zones. Finally, we should mention that regions where heart rate measurements are abnormal indicate a possible cardiac anomaly.

Keywords

• corner and jump discontinuities
• noise
• ENO and subcell-resolution approximations
• heart rate measurements
• phases of exercise