Blocking and trapping of waves in an inhomogeneous flow

Long, Steven; Lai, R. J.; Huang, Norden E.; Spedding, Geoffrey

doi:10.1016/0377-0265(93)90049-d

Cited by 21 publications

(9 citation statements)

References 12 publications

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“…There are other variations of the Fourier-based methods, such as the spectrogram (see, for example, Oppenheim & Schafer 1989); wavelet analysis for time series (see, for example, Chan 1995, Farge 1992, and Long et al 1993a, and two-dimensional images (Spedding et al 1993); the Wigner-Ville distribution (see, for example, Claasen &Mecklenbräuker 1980 andCohen 1995); the evolutionary spectrum (see, for example, Priestley 1965); the empirical orthogonal function expansion, also known as the principal component analysis, or singular value decomposition method; and some miscellaneous methods such as least square estimation of the trend, smoothing by moving averaging, and differencing to generate stationary data. All the above methods are designed to modify the global representation of the Fourier analysis, but they all failed in one way or the other, as discussed by Huang et al (1998a) and demonstrated here.…”

Section: Discussionmentioning

confidence: 99%

A NEW VIEW OF NONLINEAR WATER WAVES: The Hilbert Spectrum

Huang¹,

Shen²,

Long³

1999

Annu. Rev. Fluid Mech.

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1,872

1,100

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We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes.

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Section: Discussionmentioning

confidence: 99%

A NEW VIEW OF NONLINEAR WATER WAVES: The Hilbert Spectrum

Huang¹,

Shen²,

Long³

1999

Annu. Rev. Fluid Mech.

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1,872

1,100

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“…A review of wavelet in geosciences can be found in FoufoulaGeorgiou and Kumar (1995). This paper will concentrate on the most recent contributions in the field of earth sciences: † Fluid mechanics with isolation of coherent structures in turbulent flows (Argoul et al, 1989;Liandrat et al, 1990;Farge and Rabreau, 1988;Farge, 1992;Long et al, 1993;Higuchi et al, 1994;Katul et al, 1994Katul et al, , 1995aKatul et al, , 1995b. † Meteorology with temporal variability of coherent convective storm structures (Kumar and Foufoula-Georgiou, 1993;Takeuchi et al, 1994;Venugopal and Foufoula-Georgiou, 1996;Kumar, 1996), and examination of turbulence structures above forest canopy (Turner et al, 1994;Katul and Parlange, 1995a,b;Szilagi et al, 1999;Katul et al, 1998Katul et al, , 2001.…”

Section: The Wavelet Transform In Geosciencesmentioning

confidence: 98%

Recent advances in wavelet analyses: Part 1. A review of concepts

Labat

2005

Journal of Hydrology

499

299

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“…The well known Fourier spectral analysis works well for strictly periodic or stationary random functions of time. To deal with nonperiodic or nonstationary functions, a number of methods have been introduced, such as the Spectrogram (10), the Wavelet analysis (11)(12)(13)(14), the Wigner-Ville distribution (15,16), the Evolutionary Spectrum (17), the Modal Analysis (18), and some others, all designed to modify the global representation of the Fourier analysis. They all failed in one way or another as discussed by Huang et al (19,20).…”

Section: Materials and Experimental Methodsmentioning

confidence: 99%

Engineering analysis of biological variables: An example of blood pressure over 1 day

Huang

Shen²,

Huang³

et al. 1998

Proc. Natl. Acad. Sci. U.S.A.

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189

126

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Almost all variables in biology are nonstationarily stochastic. For these variables, the conventional tools leave us a feeling that some valuable information is thrown away and that a complex phenomenon is presented imprecisely. Here, we apply recent advances initially made in the study of ocean waves to study the blood pressure waves in the lung. We note first that, in a long wave train, the handling of the local mean is of predominant importance. It is shown that a signal can be described by a sum of a series of intrinsic mode functions, each of which has zero local mean at all times. The process of deriving this series is called the ''empirical mode decomposition method.'' Conventionally, Fourier analysis represents the data by sine and cosine functions, but no instantaneous frequency can be defined. In the new way, the data are represented by intrinsic mode functions, to which Hilbert transform can be used. Titchmarsh [Titchmarsh, E. C. (1948) Introduction to the Theory of Fourier Integrals (Oxford Univ. Press, Oxford)] has shown that a signal and i times its Hilbert transform together define a complex variable. From that complex variable, the instantaneous frequency, instantaneous amplitude, Hilbert spectrum, and marginal Hilbert spectrum have been defined. In addition, the Gumbel extremevalue statistics are applied. We present all of these features of the blood pressure records here for the reader to see how they look. In the future, we have to learn how these features change with disease or interventions.We recorded the blood pressure in the pulmonary arterial trunk (between the pulmonic valve and the bifurcation point of the right and left pulmonary arteries). The recording was done continuously with an implanted catheter as a part of a research plan to study the remodeling of the three layers of vascular tissues of the arterial wall in response to changes of stresses in the tissues (1-6). Pulmonary arteries were chosen as an object of tissue engineering research because blood pressure in pulmonary arteries can be changed quickly and noninvasively by changing the oxygen concentration in the gas that the animal breathes. Blood pressure is a major parameter related to the stress distribution in the blood vessel wall. The present article is focused on the analysis of the blood pressure records of a normal rat breathing normal atmosphere at sea level. Fig. 1A shows a record over a 24-h period. Fig. 1 B and C show segments recorded at an expanded time scale. It is seen that the amplitude and frequency are variable. The changes are nonstationary, and definitions are needed to know what the heart rate, the mean blood pressure, and the amplitude of pressure oscillations are. Our objective is to see how these quantities can be characterized mathematically. MATERIALS AND EXPERIMENTAL METHODSFor the purpose of long term recording of blood pressure, a catheter must be implanted into an artery. The Riva-Rocci cuff inflation method of blood pressure measurement based on Korotkoff sounds cannot provide the desi...

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Blocking and trapping of waves in an inhomogeneous flow

Cited by 21 publications

References 12 publications

A NEW VIEW OF NONLINEAR WATER WAVES: The Hilbert Spectrum

A NEW VIEW OF NONLINEAR WATER WAVES: The Hilbert Spectrum

Recent advances in wavelet analyses: Part 1. A review of concepts

Engineering analysis of biological variables: An example of blood pressure over 1 day

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