title: The discrete complex wavelet approach to phase assignment and a new test bed for related methods.
abstract: A new approach based on the dual-tree complex wavelet transform is introduced for phase assignment to non-linear oscillators, namely, the Discrete Complex Wavelet Approach-DCWA. This methodology is able to measure phase difference with enough accuracy to track fine variations, even in the presence of Gaussian observational noise and when only a single scalar measure of the oscillator is available. So, it can be an especially interesting tool to deal with experimental data. In order to compare it with other phase detection techniques, a testbed is introduced. This testbed provides time series from dynamics similar to non-linear oscillators, such that a theoretical phase choice is known in advance. Moreover, it allows to tune different types of phase synchronization to test phase detection methods under a variety of scenarios. Through numerical benchmarks, we report that the proposed approach is a reliable alternative and that it is particularly effective compared with other methodologies in the presence of moderate to large noises.
authors: Laboratory of Computing and Applied Mathematics - LAC, Brazilian National Institute for Space Research - INPE, São José dos Campos, Brazil.
authors: Maria Teodora
authors: MT
authors: Ferreira
authors: Laboratory of Computing and Applied Mathematics - LAC, Brazilian National Institute for Space Research - INPE, São José dos Campos, Brazil.
authors: Celso Bernardo
authors: CB
authors: Nóbrega Freitas
authors: Laboratory of Computing and Applied Mathematics - LAC, Brazilian National Institute for Space Research - INPE, São José dos Campos, Brazil.
authors: Margarete O
authors: MO
authors: Domingues
authors: Laboratory of Computing and Applied Mathematics - LAC, Brazilian National Institute for Space Research - INPE, São José dos Campos, Brazil.
authors: Elbert E N
authors: EE
authors: Macau