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Zhaohua Wu

Bio: Zhaohua Wu is an academic researcher from Florida State University. The author has contributed to research in topics: Hilbert–Huang transform & Annual cycle. The author has an hindex of 33, co-authored 75 publications receiving 12645 citations. Previous affiliations of Zhaohua Wu include Nanjing University & State Oceanic Administration.


Papers
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Journal ArticleDOI
TL;DR: The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF.
Abstract: A new Ensemble Empirical Mode Decomposition (EEMD) is presented. This new approach consists of sifting an ensemble of white noise-added signal (data) and treats the mean as the final true result. Finite, not infinitesimal, amplitude white noise is necessary to force the ensemble to exhaust all possible solutions in the sifting process, thus making the different scale signals to collate in the proper intrinsic mode functions (IMF) dictated by the dyadic filter banks. As EEMD is a time–space analysis method, the added white noise is averaged out with sufficient number of trials; the only persistent part that survives the averaging process is the component of the signal (original data), which is then treated as the true and more physical meaningful answer. The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF. With this ensemble mean, one can separate scales naturall...

6,437 citations

Journal ArticleDOI
TL;DR: In this article, empirical experiments on white noise using the empirical mode decomposition (EMD) method were conducted and it was shown empirically that the EMD is effectively a dyadic filter, the intrinsic mode function (IMF) components are all normally distributed, and the Fourier spectra of the IMF components cover the same area on a semi-logarithmic period scale.
Abstract: Based on numerical experiments on white noise using the empirical mode decomposition (EMD) method, we find empirically that the EMD is effectively a dyadic filter, the intrinsic mode function (IMF) components are all normally distributed, and the Fourier spectra of the IMF components are all identical and cover the same area on a semi–logarithmic period scale. Expanding from these empirical findings, we further deduce that the product of the energy density of IMF and its corresponding averaged period is a constant, and that the energy–density function is chi–squared distributed. Furthermore, we derive the energy–density spread function of the IMF components. Through these results, we establish a method of assigning statistical significance of information content for IMF components from any noisy data. Southern Oscillation Index data are used to illustrate the methodology developed here.

1,573 citations

Journal ArticleDOI
TL;DR: Hilbert-Huang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research.
Abstract: [1] Data analysis has been one of the core activities in scientific research, but limited by the availability of analysis methods in the past, data analysis was often relegated to data processing. To accommodate the variety of data generated by nonlinear and nonstationary processes in nature, the analysis method would have to be adaptive. Hilbert-Huang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research. In this review, we will briefly introduce the method, list some recent developments, demonstrate the usefulness of the method, summarize some applications in various geophysical research areas, and finally, discuss the outstanding open problems. We hope this review will serve as an introduction of the method for those new to the concepts, as well as a summary of the present frontiers of its applications for experienced research scientists.

1,533 citations

Journal ArticleDOI
TL;DR: A simple and logical definition of trend is given for any nonlinear and nonstationary time series as an intrinsically determined monotonic function within a certain temporal span, or a function in which there can be at most one extremum within that temporal span.
Abstract: Determining trend and implementing detrending operations are important steps in data analysis. Yet there is no precise definition of “trend” nor any logical algorithm for extracting it. As a result, various ad hoc extrinsic methods have been used to determine trend and to facilitate a detrending operation. In this article, a simple and logical definition of trend is given for any nonlinear and nonstationary time series as an intrinsically determined monotonic function within a certain temporal span (most often that of the data span), or a function in which there can be at most one extremum within that temporal span. Being intrinsic, the method to derive the trend has to be adaptive. This definition of trend also presumes the existence of a natural time scale. All these requirements suggest the Empirical Mode Decomposition (EMD) method as the logical choice of algorithm for extracting various trends from a data set. Once the trend is determined, the corresponding detrending operation can be implemented. With this definition of trend, the variability of the data on various time scales also can be derived naturally. Climate data are used to illustrate the determination of the intrinsic trend and natural variability.

787 citations

Journal ArticleDOI
TL;DR: This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing IF, and finds that the NHT and direct quadrature gave the best overall performance.
Abstract: Instantaneous frequency (IF) is necessary for understanding the detailed mechanisms for nonlinear and nonstationary processes. Historically, IF was computed from analytic signal (AS) through the Hilbert transform. This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing IF. The first approach is to compute the quadrature (defined here as a simple 90° shift of phase angle) directly. The second approach is designated as the normalized Hilbert transform (NHT), which consists of applying the Hilbert transform to the empirically determined FM signals. Additionally, we have also introduced alternative methods to compute local frequency, the generalized zero-crossing (GZC), and the teager energy operator (TEO) methods. Through careful comparisons, we found that the NHT and direct quadrature gave the best overall performance. While the TEO method is the most localized, it is limited to data from linear processes, the GZC method is the m...

618 citations


Cited by
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Journal ArticleDOI
TL;DR: The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF.
Abstract: A new Ensemble Empirical Mode Decomposition (EEMD) is presented. This new approach consists of sifting an ensemble of white noise-added signal (data) and treats the mean as the final true result. Finite, not infinitesimal, amplitude white noise is necessary to force the ensemble to exhaust all possible solutions in the sifting process, thus making the different scale signals to collate in the proper intrinsic mode functions (IMF) dictated by the dyadic filter banks. As EEMD is a time–space analysis method, the added white noise is averaged out with sufficient number of trials; the only persistent part that survives the averaging process is the component of the signal (original data), which is then treated as the true and more physical meaningful answer. The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF. With this ensemble mean, one can separate scales naturall...

6,437 citations

Journal ArticleDOI
TL;DR: This work proposes an entirely non-recursive variational mode decomposition model, where the modes are extracted concurrently and is a generalization of the classic Wiener filter into multiple, adaptive bands.
Abstract: During the late 1990s, Huang introduced the algorithm called Empirical Mode Decomposition, which is widely used today to recursively decompose a signal into different modes of unknown but separate spectral bands. EMD is known for limitations like sensitivity to noise and sampling. These limitations could only partially be addressed by more mathematical attempts to this decomposition problem, like synchrosqueezing, empirical wavelets or recursive variational decomposition. Here, we propose an entirely non-recursive variational mode decomposition model, where the modes are extracted concurrently. The model looks for an ensemble of modes and their respective center frequencies, such that the modes collectively reproduce the input signal, while each being smooth after demodulation into baseband. In Fourier domain, this corresponds to a narrow-band prior. We show important relations to Wiener filter denoising. Indeed, the proposed method is a generalization of the classic Wiener filter into multiple, adaptive bands. Our model provides a solution to the decomposition problem that is theoretically well founded and still easy to understand. The variational model is efficiently optimized using an alternating direction method of multipliers approach. Preliminary results show attractive performance with respect to existing mode decomposition models. In particular, our proposed model is much more robust to sampling and noise. Finally, we show promising practical decomposition results on a series of artificial and real data.

4,111 citations

Journal ArticleDOI
TL;DR: It turns out that EMD acts essentially as a dyadic filter bank resembling those involved in wavelet decompositions, and the hierarchy of the extracted modes may be similarly exploited for getting access to the Hurst exponent.
Abstract: Empirical mode decomposition (EMD) has recently been pioneered by Huang et al. for adaptively representing nonstationary signals as sums of zero-mean amplitude modulation frequency modulation components. In order to better understand the way EMD behaves in stochastic situations involving broadband noise, we report here on numerical experiments based on fractional Gaussian noise. In such a case, it turns out that EMD acts essentially as a dyadic filter bank resembling those involved in wavelet decompositions. It is also pointed out that the hierarchy of the extracted modes may be similarly exploited for getting access to the Hurst exponent.

2,304 citations

Journal ArticleDOI
TL;DR: The Madden-Julian Oscillation (MJO) is the dominant component of the intraseasonal (30-90 days) variability in the tropical atmosphere as mentioned in this paper, which consists of large-scale coupled patterns in atmospheric circulation and deep convection with coherent signals in many other variables, all propagating eastward slowly through the portion of the Indian and Pacific oceans where the sea surface is warm.
Abstract: [1] The Madden-Julian Oscillation (MJO) is the dominant component of the intraseasonal (30–90 days) variability in the tropical atmosphere. It consists of large-scale coupled patterns in atmospheric circulation and deep convection, with coherent signals in many other variables, all propagating eastward slowly (∼5 m s−1) through the portion of the Indian and Pacific oceans where the sea surface is warm. It constantly interacts with the underlying ocean and influences many weather and climate systems. The past decade has witnessed an expeditious progress in the study of the MJO: Its large-scale and multiscale structures are better described, its scale interaction is recognized, its broad influences on tropical and extratropical weather and climate are increasingly appreciated, and its mechanisms for disturbing the ocean are further comprehended. Yet we are facing great difficulties in accurately simulating and predicting the MJO using sophisticated global weather forecast and climate models, and we are unable to explain such difficulties based on existing theories of the MJO. It is fair to say that the MJO remains an unmet challenge to our understanding of the tropical atmosphere and to our ability to simulate and predict its variability. This review, motivated by both the acceleration and gaps in our knowledge of the MJO, intends to synthesize what we currently know and what we do not know on selected topics: its observed basic characteristics, mechanisms, numerical modeling, air-sea interaction, and influences on the El Nino and Southern Oscillation.

1,931 citations

Journal ArticleDOI
TL;DR: This paper introduces a precise mathematical definition for a class of functions that can be viewed as a superposition of a reasonably small number of approximately harmonic components, and proves that the method does indeed succeed in decomposing arbitrary functions in this class.

1,704 citations