Applying the Hilbert--Huang Decomposition to Horizontal Light Propagation C_n^2 data

The Hilbert Huang Transform is a new technique for the analysis of non--stationary signals. It comprises two distinct parts: Empirical Mode Decomposition (EMD) and the Hilbert Transform of each of the modes found from the first step to produce a Hilbert Spectrum. The EMD is an adaptive decomposition of the data, which results in the extraction of Intrinsic Mode Functions (IMFs). We discuss the application of the EMD to the calibration of two optical scintillometers that have been used to measure C_n^2 over horizontal paths on a building rooftop, and discuss the advantage of using the Marginal Hilbert Spectrum over the traditional Fourier Power Spectrum.Comment: 9 pages, 11 figures, proc. SPIE 626

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

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 extreme-value 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

Using Empirical Mode Decomposition (EMD) for the processing of marine MT data

Magnetotelluric (MT) method determines a frequency dependent impedance tensor using the spectra of associated time-varying horizontal electric and magnetic fields measured at the Earth’s surface. In this abstract, we present a dynamic time series analysis method dealing the non-stationary MT data to infer the impedance tensor. Most current methods to determine the spectra use Fourier transform based procedure and, therefore, assume that the signals are stationary over the record length. We introduce a new method for dealing with non-stationarity of the MT time series based upon empirical mode decomposition (EMD) method, a dynamic time series analysis method. Using EMD complicated data sets can be decomposed into a finite and small number of "intrinsic mode functions" (IMFs), which are mono-component signals and allow the calculation of physical meaningful instantaneous frequencies. EMD has no bias due to non-stationary of geomagnetic time series, since the IMFs are based entirely on signal characteristics and not on any given set of base functions such as sines and cosines in the Fourier transform or wavelets in the Wavelet transform. We use the EMD method to decompose MT data into IMFs and calculate the instantaneous frequencies and spectra to determine the impedance tensor. The method is tested in synthetic and real marine MT data sets, the obtained estimate results are reliable compared to frequently-used BIRRP processing method. Furthermore, new method has the possibility of noise visualization and filtering, which is especially important in marine applications, where noise free time segments maybe short

Lagrangian single particle turbulent statistics through the Hilbert-Huang Transform

The Hilbert-Huang transform is applied to analyze single particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions, C_{i}(t), and of their instantaneous frequency, \omega_{i}(t). On the basis of this decomposition we define the \omega-conditioned statistical moments of the C_{i} modes, named q-order Hilbert Spectra (HS). We show that such new quantities have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (Structure Functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present a clear empirical evidence that the energy-like quantity, i.e. the second-order HS, displays a linear scaling in time in the inertial range, as expected from dimensional analysis and never observed before. We also measure high order moment scaling exponents in a direct way, without resorting the Extended Self Similarity (ESS) procedure. This leads to a new estimate of the Lagrangian structure functions exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed in [Biferale et al., Phys. Rev. Lett. vol. 93, 064502 (2004)].Comment: 5 pages, 5 figure

Empirical mode decomposition of wind speed signals

Empirical Mode Decomposition (EMD) is a powerful signal processing technique with diverse applications, particularly in the analysis of non-stationary data. In this study, we assess the capabilities of EMD for wind data analysis, aiming to uncover its effectiveness in capturing intricate temporal patterns and decomposing data into Intrinsic Mode Functions (IMFs) to identify crucial frequency components. Various methods of sifting have been studied as the IMFs and therefore results may vary according to the type. It has been concluded that the Ensemble Empirical Mode Decomposition (EEMD) is the most suitable method for these data. A comparison with Fourier analysis is also conducted to elucidate the strengths and limitations of each method. Furthermore, this investigation examines the Average Diurnal Variation (ADV) and Average Seasonal Variation (ASV) patterns within the wind data. It is found that these patters have a physical significance and interpretation of the IMFs and that it is easier to use EMD than Fourier for wind signals

Crystal image analysis using 2D2D synchrosqueezed transforms

We propose efficient algorithms based on a band-limited version of 2D synchrosqueezed transforms to extract mesoscopic and microscopic information from atomic crystal images. The methods analyze atomic crystal images as an assemblage of non-overlapping segments of 2D general intrinsic mode type functions, which are superpositions of non-linear wave-like components. In particular, crystal defects are interpreted as the irregularity of local energy; crystal rotations are described as the angle deviation of local wave vectors from their references; the gradient of a crystal elastic deformation can be obtained by a linear system generated by local wave vectors. Several numerical examples of synthetic and real crystal images are provided to illustrate the efficiency, robustness, and reliability of our methods.Comment: 27 pages, 17 figure