ZeChipC: Time Series Interpolation Method Based on Lebesgue Sampling

Abstract

In this paper, we present an interpolation method based on Lebesgue sampling that could help to develop systems based time series more efficiently. Our methods can transmit times series, frequently used in health monitoring, with the same level of accuracy but using much fewer data. Our method is based in Lebesgue sampling, which collects information depending on the values of the signal (e.g. the signal output is sampled when it crosses specific limits). Lebesgue sampling contains additional information about the shape of the signal in-between two sampled points. Using this information would allow generating an interpolated signal closer to the original one. In our contribution, we propose a novel time-series interpolation method designed explicitly for Lebesgue sampling called ZeChipC. ZeChipC is a combination of Zero-order hold and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) interpolation. ZeChipC includes new functionality to adapt the reconstructed signal to concave/convex regions. The proposed methods have been compared with state-of-the-art interpolation methods using Lebesgue sampling and have offered higher average performance.