### Аннотация

This paper is devoted to an unexplored discrete optimization problem, which can be interpreted as a problem of least mean squares approximation of some observed discrete-time signal (a numerical time series) by an unobservable quasiperiodic (almost periodic) pulse signal generated by a pulse with a given pattern (reference) shape. Quasiperiodicity is understood, first, in the sense of admissible fluctuations of the interval between repetitions of the reference pulse, and second, in the sense of admissible nonlinear time expansions of its reference shape. Such problems are common in biomedical applications related to monitoring and analyzing electrocardiogram (ECG), photoplethysmogram (PPG), and several other signals. In the optimization model, the number of generated (admissible or approximating) quasiperiodic pulse sequences grows exponentially with the duration of the discrete-time signal (i.e., with the number of points in the time series). The size of the admissible solutions set also grows exponentially. However, despite that exponential growth, we have constructively proved the optimization problem polynomial-time solvability. Namely, we propose an algorithm that finds an optimal solution to the problem in (formula presented) time; where N is the duration of the observed signal (the number of points in the time series), (formula presented) is a positive integer number which bounds the fluctuations of the repetition period. If (formula presented) is a part of the input, then the algorithm’s running time is (formula presented), i.e., the algorithm is polynomial. If (formula presented) is a fixed parameter (that is typical for applications), then the running-time of the algorithm is (formula presented), i.e., the algorithm is linear in time. Numerical simulation examples demonstrate the robustness of the algorithm in the presence of additive noise.

Язык оригинала | английский |
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Название основной публикации | Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers |

Редакторы | Milojica Jaćimović, Michael Khachay, Vlasta Malkova, Mikhail Posypkin |

Издатель | Springer Gabler |

Страницы | 88-101 |

Число страниц | 14 |

ISBN (печатное издание) | 9783030386023 |

DOI | |

Состояние | Опубликовано - 1 янв 2020 |

Событие | 10th International Conference on Optimization and Applications, OPTIMA 2019 - Petrovac, Черногория Продолжительность: 30 сен 2019 → 4 окт 2019 |

### Серия публикаций

Название | Communications in Computer and Information Science |
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Том | 1145 CCIS |

ISSN (печатное издание) | 1865-0929 |

ISSN (электронное издание) | 1865-0937 |

### Конференция

Конференция | 10th International Conference on Optimization and Applications, OPTIMA 2019 |
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Страна | Черногория |

Город | Petrovac |

Период | 30.09.2019 → 04.10.2019 |

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### Цитировать

*Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers*(стр. 88-101). (Communications in Computer and Information Science; Том 1145 CCIS). Springer Gabler. https://doi.org/10.1007/978-3-030-38603-0_7