Wave-shape oscillatory model for nonstationary periodic time series analysis

Lin, Yuting; Malik, John; Wu, Hau‐Tieng

doi:10.3934/fods.2021009

Cited by 20 publications

(17 citation statements)

References 52 publications

(92 reference statements)

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“…There also exist optimization approaches to decompose the signal [48,50], and dynamic diffusion maps to recover the intrinsic dynamics [21]. We shall mention that while not motivated and developed based on the idea of WSF, the periodicity transform [35,42] and its generalization to time-frequency domain [10] are another approaches that have been developed to handle similar non-sinusoidal oscillatory signals.…”

Section: Date: August 16 2022mentioning

confidence: 99%

“…While there have been several efforts put in this research direction, however, to our knowledge, so far there is limited work focusing on handling the case when the WSF would suddenly change from one pattern to a dramatically different pattern, except a stretch of the wave-shape oscillatory model [21] and a simplified oscillatory change point detection model [51]. This sudden change phenomenon is commonly encountered in practice, in particular in the biomedical signal processing field.…”

Section: Date: August 16 2022mentioning

confidence: 99%

“…In the past decade, this non-sinusoidal oscillation phenomenon and the WSF model have attracted more and more attention [41,18,48,50], and several variations of the original WSF model have been proposed to capture finer structures hidden inside the WSF; for example, the sparse time-frequency representation [41], a generalization of WSF (this model is abbreviated as WSFv2 hereafter) to capture time-varying oscillatory pattern [20] and the wave-shape oscillatory model [21]. Based on the above mentioned WSF model and its variations, various algorithms have been developed to study the signal facing different challenges; for example, the algorithm based on the sparse time-frequency representation method extracts intrinsic frequency information and defines the notion of degree of nonlinearity [41,18], the de-shape algorithm based on WSFv2 reduces the impact of harmonics [20], the linear regression approach based on WSFv1 recovers the WSF and it is useful to estimate the order of a waveform [47,34], the nonlinear regression approach based on WSFv2 decomposes signals with time-varying waveforms [11].…”

Section: Introductionmentioning

confidence: 99%

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An iterative warping and clustering algorithm to estimate multiple wave-shape functions from a nonstationary oscillatory signal

Colominas¹,

Wu²

2022

Preprint

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We present an algorithm to estimate multiple wave-shape functions (WSF) from a nonstationary oscillatory signal with time-varying amplitude and frequency. Suppose there are finite different 1-periodic functions, s 1 , . . . , s K , as WSFs that model different oscillatory patterns in an oscillatory signal, where the WSF might jump from one to another suddenly. The proposed algorithm detects change points and estimates s 1 , . . . , s K from the signal by a novel iterative warping and clustering algorithm, which is a combination of time-frequency analysis, singular value decomposition entropy and vector spectral clustering. We demonstrate the efficiency of the proposed algorithm with simulated and real signals, including the voice signal, arterial blood pressure, electrocardiogram and accelerometer signal. Moreover, we provide a mathematical justification of the algorithm under the assumption that the amplitude and frequency of the signal are slowly time-varying and there are finite change points that model sudden changes from one wave-shape function to another one.

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Section: Date: August 16 2022mentioning

confidence: 99%

Section: Date: August 16 2022mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An iterative warping and clustering algorithm to estimate multiple wave-shape functions from a nonstationary oscillatory signal

Colominas¹,

Wu²

2022

Preprint

Self Cite

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“…Before closing this section, we mention that in 2019, inspired by analyzing pathophysiological signals, the manifold model was considered to further generalize the ANHM. Specifically, we view each oscillation as a point on a manifold, which is called the wave-shape manifold [83]. The recorded signal is then viewed as a realization of the trajectory on the manifold.…”

Section: Modelmentioning

confidence: 99%

Current state of nonlinear-type time-frequency analysis and applications to high-frequency biomedical signals

2020

Preprint

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“…We shall mention that there have been several generalizations, e.g. the time-varying WSF [48] and wave-shape manifold [50], to better capture the biomedical signals (see more in [36]). To simplify the discussion, we focus on Definition 1.…”

Section: What Is Phase? From Old To Newmentioning

confidence: 99%

Reconsider phase reconstruction in signals with dynamic periodicity from the modern signal processing perspective

Alian

Lo²,

Shelley

et al. 2020

Preprint

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Phase is the most fundamental physical quantity when we study an oscillatory time series, and there are a lot of tools aiming to estimate phase. Most existing tools are developed based on the well-developed analytic function model. Unfortunately, this approach might not be suitable for several modern signals, particularly biomedical signals, due to the intrinsic complicated structure, and the lack of standard methods on how to estimate phases. Specifically, different recording equipment for the same physiological system might lead to different phases based on existing tools, and the same recording equipment for different subjects might vary from subject to subject, even if the cycling periods are the same. The lack of consensus, or standard, might lead to the challenge of reproducibility, communication, and scientific interpretation. In face of this challenge, we propose the use of the recently developed adaptive non-harmonic model and synchrosqueezing transformation to standardize the phase information extraction. To illustrate the scientific impact of the proposed standardization and tools, we show analysis results in two different physiological signals with clinical applications.

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Wave-shape oscillatory model for nonstationary periodic time series analysis

Cited by 20 publications

References 52 publications

An iterative warping and clustering algorithm to estimate multiple wave-shape functions from a nonstationary oscillatory signal

An iterative warping and clustering algorithm to estimate multiple wave-shape functions from a nonstationary oscillatory signal

Current state of nonlinear-type time-frequency analysis and applications to high-frequency biomedical signals

Reconsider phase reconstruction in signals with dynamic periodicity from the modern signal processing perspective

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