### Abstract

We propose a method for phase estimation of a single non-parametric quasi-periodic signal. Assuming signal intensities should be equal among samples of the same phase, such corresponding samples are obtained by self-dynamic time warping between a quasi-periodic signal and a signal with multiple-period shifts applied. A phase sequence is then estimated in a sub-sampling order using an optimization framework incorporating 1) a data term derived from the correspondences and 2) a smoothness term of the local phase evolution under 3) a monotonic-increasing constraint on the phase. Such a phase estimation is, however, ill-posed because of combination ambiguity between the phase evolution and the normalized periodic signal, and hence can result in a biased solution. Therefore, we introduce into the optimization framework 4) a bias correction term, which imposes zero-bias from the linear phase evolution. Analysis of the quasi-periodic signals from both simulated and real data indicate the effectiveness and also potential applications of the proposed method.

Original language | English |
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Article number | 6740000 |

Pages (from-to) | 2066-2079 |

Number of pages | 14 |

Journal | IEEE Transactions on Signal Processing |

Volume | 62 |

Issue number | 8 |

DOIs | |

Publication status | Published - Apr 15 2014 |

### All Science Journal Classification (ASJC) codes

- Signal Processing
- Electrical and Electronic Engineering

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## Cite this

*IEEE Transactions on Signal Processing*,

*62*(8), 2066-2079. [6740000]. https://doi.org/10.1109/TSP.2014.2306174