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RANDOM DATA Analysis and Measurement Procedures
01 Jan 1971-
TL;DR: A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems, is presented in this article.
Abstract: From the Publisher:
A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems. With more than 100,000 copies in print and six foreign translations, the first edition standardized the methodology in this field. This new edition covers all new procedures developed since 1971 and extends the application of random data analysis to aerospace and automotive research; digital data analysis; dynamic test programs; fluid turbulence analysis; industrial noise control; oceanographic data analysis; system identification problems; and many other fields. Includes new formulas for statistical error analysis of desired estimates, new examples and problem sets.
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TL;DR: In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.
Abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...
18,956 citations
Cites background from "RANDOM DATA Analysis and Measuremen..."
...A brief tutorial on the Hilbert transform with the emphasis on its physical interpretation can be found in Bendat & Piersol (1986)....
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TL;DR: A new and related complexity measure is developed, sample entropy (SampEn), and a comparison of ApEn and SampEn is compared by using them to analyze sets of random numbers with known probabilistic character, finding SampEn agreed with theory much more closely than ApEn over a broad range of conditions.
Abstract: Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.
6,088 citations
Cites background or methods from "RANDOM DATA Analysis and Measuremen..."
...0, we found that cross-ApEn(1,1,250)(cv\hr) was defined for only 19 of the 32 cases, whereas cross-ApEn(1,1,250)(hr \cv) was defined for only 12 cases....
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...Sets of uniformly distributed random numbers were generated using a minimal standard number generator with added random shuffling (30), and all sets passed a runs test for random arrangement (1)....
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TL;DR: It is concluded that changes in the earth's orbital geometry are the fundamental cause of the succession of Quaternary ice ages and a model of future climate based on the observed orbital-climate relationships, but ignoring anthropogenic effects, predicts that the long-term trend over the next sevem thousand years is toward extensive Northern Hemisphere glaciation.
Abstract: 1) Three indices of global climate have been monitored in the record of the past 450,000 years in Southern Hemisphere ocean-floor sediments. 2) Over the frequency range 10(-4) to 10(-5) cycle per year, climatic variance of these records is concentrated in three discrete spectral peaks at periods of 23,000, 42,000, and approximately 100,000 years. These peaks correspond to the dominant periods of the earth's solar orbit, and contain respectively about 10, 25, and 50 percent of the climatic variance. 3) The 42,000-year climatic component has the same period as variations in the obliquity of the earth's axis and retains a constant phase relationship with it. 4) The 23,000-year portion of the variance displays the same periods (about 23,000 and 19,000 years) as the quasi-periodic precession index. 5) The dominant, 100,000-year climatic [See table in the PDF file] component has an average period close to, and is in phase with, orbital eccentricity. Unlike the correlations between climate and the higher-frequency orbital variations (which can be explained on the assumption that the climate system responds linearly to orbital forcing), an explanation of the correlation between climate and eccentricity probably requires an assumption of nonlinearity. 6) It is concluded that changes in the earth's orbital geometry are the fundamental cause of the succession of Quaternary ice ages. 7) A model of future climate based on the observed orbital-climate relationships, but ignoring anthropogenic effects, predicts that the long-term trend over the next sevem thousand years is toward extensive Northern Hemisphere glaciation.
3,408 citations
TL;DR: In this paper, an improved estimation of mesoscale surface ocean circulation was obtained by merging TOPEX/Poseidon (T/P) and ERS-1 and -2 altimeter measurements between October 1992 and May 1998.
Abstract: This study focuses on the improved estimation of mesoscale surface ocean circulation obtained by merging TOPEX/Poseidon (T/P) and ERS-1 and -2 altimeter measurements between October 1992 and May 1998. Once carefully intercalibrated and homogenized, these data are merged through an advanced global objective analysis method that allows us to correct for residual long wavelength errors and uses realistic correlation scales of ocean dynamics. The high-resolution (0.25°×0.25°) merged T/P+ERS-1 and -2 sea level anomaly maps provide more homogeneous and reduced mapping errors than either individual data set and more realistic sea level and geostrophic velocity statistics than T/P data alone. Furthermore, the merged T/P+ERS-1 and -2 maps yield eddy kinetic energy (EKE) levels 30% higher than maps of T/P alone. They also permit realistic global estimates of east and north components of EKE and their seasonal variations, to study EKE sources better. A comparison of velocity statistics with World Ocean Circulation Experiment surface drifters in the North Atlantic shows very good agreement. Comparison with contemporary current meter data in various oceanic regimes also produces comparable levels of energy and similar ratios of northward and eastward energy, showing that the maps are suitable to studying anisotropy. The T/P + ERS zonal and meridional components of the mapped currents usually present comparable rms variability, even though the variability in the Atlantic is more isotropic than that in the Pacific, which exhibits strong zonal changes. The EKE map presents a very detailed description, presumably never before achieved at a global scale. Pronounced seasonal changes of the EKE are found in many regions, notably the northeastern Pacific, the northeastern and northwestern Atlantic, the tropical oceans, and the zonally extended bands centered near 20°S in the Indian and western Pacific Oceans and at 20°N in the northwestern Pacific.
1,575 citations
TL;DR: The results suggest that long-term control of complex prosthetic robot arm movements can be achieved by simple real-time transformations of neuronal population signals derived from multiple cortical areas in primates.
Abstract: Signals derived from the rat motor cortex can be used for controlling one-dimensional movements of a robot arm1. It remains unknown, however, whether real-time processing of cortical signals can be employed to reproduce, in a robotic device, the kind of complex arm movements used by primates to reach objects in space. Here we recorded the simultaneous activity of large populations of neurons, distributed in the premotor, primary motor and posterior parietal cortical areas, as non-human primates performed two distinct motor tasks. Accurate real-time predictions of one- and three-dimensional arm movement trajectories were obtained by applying both linear and nonlinear algorithms to cortical neuronal ensemble activity recorded from each animal. In addition, cortically derived signals were successfully used for real-time control of robotic devices, both locally and through the Internet. These results suggest that long-term control of complex prosthetic robot arm movements can be achieved by simple real-time transformations of neuronal population signals derived from multiple cortical areas in primates.
1,435 citations