Wigner-Ville spectral analysis of nonstationary processes

Martin, Wolfgang; Flandrin, Patrick

doi:10.1109/tassp.1985.1164760

Cited by 491 publications

(239 citation statements)

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“…This has been used in the context of signal processing for non-stationary random processes (Martin and Flandrin 1985) and for the propagation of waves in random media (Bal et al 2003;Ryzhik et al 1996;Erdös and Yau 2000). In the context of water waves, Alber (1978) used the Wigner spectrum to study the directional stability of solutions of the two-dimensional Davey-Stewartson equations in a narrowband setting.…”

Section: Observe That W [U(t)](x K) Is Real Valued For Any Complex Vmentioning

confidence: 99%

Localized instabilities of the Wigner equation as a model for the emergence of Rogue Waves

Athanassoulis

Sapsis

2017

J. Ocean Eng. Mar. Energy

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In this paper, we model Rogue Waves as localized instabilities emerging from homogeneous and stationary background wavefields, under NLS dynamics. This is achieved in two steps: given any background Fourier spectrum P(k), we use the Wigner transform and Penrose's method to recover spatially periodic unstable modes, which we call unstable Penrose modes. These can be seen as generalized Benjamin-Feir modes, and their parameters are obtained by resolving the Penrose condition, a system of nonlinear equations involving P(k). Moreover, we show how the superposition of unstable Penrose modes can result in the appearance of localized unstable modes. By interpreting the appearance of an unstable mode localized in an area not larger than a reference wavelength λ 0 as the emergence of a Rogue Wave, a criterion for the emergence of Rogue Waves is formulated. Our methodology is applied to δ spectra, where the standard Benjamin-Feir instability is recovered, and to more general spectra. In that context, we present a scheme for the numerical resolution of the Penrose condition and estimate the sharpest possible localization of unstable modes.B A. G. Athanassoulis

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Section: Observe That W [U(t)](x K) Is Real Valued For Any Complex Vmentioning

confidence: 99%

Localized instabilities of the Wigner equation as a model for the emergence of Rogue Waves

Athanassoulis

Sapsis

2017

J. Ocean Eng. Mar. Energy

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“…The smoothed pseudo Wigner-Ville distribution (SP-WVD) was applied to m(n) to estimate the time-varying spectral properties of both HRV signals [9], with the same parameters used in [10]. The instantaneous power in the low and high frequency band, P LF (n) and P LF (n) respectively, was extracted throughout the entire exercise test.…”

Section: Discussionmentioning

confidence: 99%

Comparison of Heart Rate Variability Assessment During Exercise from Polar RS800 and ECG

Hernando

Garatachea

Bailón

2017

Computing in Cardiology Conference (CinC)

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There are several mobile and easy to use heart rate monitors which which allow heart rate variability (HRV) IntroductionHeart rate variability (HRV) remains a powerful source for autonomic nervous system (ANS) assessment by using simple and non-invasive techniques. It is used in both clinical and research environments and over a broad spectrum of disciplines concerned with autonomic control of the heart ranging from cardiology to psychology. Advances in technology have allowed the development of mobile and easy to use heart rate monitors that allow the quantification of inter-beat intervals (RR intervals) and thus the analysis of heart rate variability. Commercial devices (like Polar, Garmin, Tomtom, or Suunto heart rate monitors, among others) appear as a cheaper alternative, usually providing software which allows for an affordable and a user-friendly method to determine short-term HRV outside of the laboratory setting.These heart rate monitors have been used by scientists for HRV analysis in sport sciences, medicine and other fields of research [1][2][3]. Several studies have validated these devices against different ECG systems, showing promising results at rest [4][5][6]. However, there are very few studies that validate HRV measurements from heart rate monitor devices during dynamic exercise of high intensity, which is characterized by a higher level of noise than in static exercise, larger variations in mean heart rate (HR) and respiratory frequency and the appearance of cardiolocomotor coupling (CC) components during high intensities.In a previous study [12], we evaluated the agreement and reliability between the HRV analysis derived from the RR series recorded by the HR monitor Polar RS800 and HRV analysis derived from a simultaneous ECG during dynamic exercise of low, medium and high intensity. At rest, Polar measurements showed high agreement and reliability indices as expected. During high intensities of exercise, however, high frequency (HF) parameters showed low agreement.The aim of this study is to evaluate changes in ANS during high intensity exercise using Polar measurements, despite the low agreement in HF parameters, to see whether the same information can be extracted than from measure-

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“…A conceptually simple time-varying estimation method consists of masking some regions of the signals' TF representations. However, this process is, in general, highly nonlinear [15], [17], resulting in difficulties especially when dealing with multicomponent signals. There are linear estimation operators based on linear time-frequency representations, but their performance generally depends on the window and wavelet used.…”

Section: B Related Workmentioning

confidence: 99%