Emd of Gaussian White Noise: Effects of Signal Length and Sifting Number on the Statistical Properties of Intrinsic Mode Functions

Schlotthauer, Gastón; Torres, Marı́a E.; Rufiner, Hugo Leonardo; Flandrin, Patrick

doi:10.1142/s1793536909000217

Cited by 20 publications

(18 citation statements)

References 7 publications

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“…The shape of h(n) is largely dependent on the signal type, sampling rate, and noise power. This finding is counter to previous suggestions that the IMFs are Gaussian and Laplacian distributions [8]- [10].…”

Section: A Analysis Of Imf Probability Distributionscontrasting

confidence: 99%

“…The statistical characteristics of the IMFs were previously investigated [8], [10], [11]. However, these investigations were limited to a comparison of the IMF distributions not an analysis of the EMD sifting process.…”

Section: A Analysis Of Imf Probability Distributionsmentioning

confidence: 99%

“…Flandrin et al analyzed fractional Gaussian noise and came to a similar conclusion about the IMF distributions [9]. However, Schlotthauer et distribution or a multimodal probability density function (PDF) rather than a Gaussian for few cases [10].…”

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confidence: 90%

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A De-noising Scheme Based on the Null Hypothesis of Intrinsic Mode Functions

Al-Badrawi

Al-Jewad

Smith

et al. 2016

IEEE Signal Process. Lett.

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Empirical mode decomposition is a nonparametric adaptive tool that decomposes signals into a set of zero-mean modes called intrinsic mode functions (IMFs) that can be used to denoise a signal by selecting the relevant (noise-free) modes. In this paper, the statistical properties of IMFs, produced by a range of signal distributions, are examined. Insight from the statistical analysis is used in a null hypothesis test that validates a best fit model distribution of the IMFs. This test is then used in a de-noising scheme, which is evaluated using different test signals corrupted with white and colored noise. Simulations under different scenarios demonstrate the efficacy of the proposed method as compared to other EMD-based de-noising techniques. Index Terms-Empirical mode decomposition (EMD), intrinsic mode function (IMF), null hypothesis, signal de-noising.1070-9908

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Section: A Analysis Of Imf Probability Distributionscontrasting

confidence: 99%

Section: A Analysis Of Imf Probability Distributionsmentioning

confidence: 99%

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A De-noising Scheme Based on the Null Hypothesis of Intrinsic Mode Functions

Al-Badrawi

Al-Jewad

Smith

et al. 2016

IEEE Signal Process. Lett.

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“…In the past, several investigations have been carried out in order to identify the effects of the EMD when applied to time series issued from various models, such as white, red, or fractional Gaussian noise, (Huang et al, 2003;Flandrin et al, 2004aFlandrin et al, , 2005Wu and Huang, 2004;Rilling et al, 2005;Schlotthauer et al, 2009;Colominas et al, 2012). As a result, it has been consistently shown that, irrespective of the assumed noise model, the EMD acts as an efficient wavelet-like dyadic filter, decomposing the stochastic inputs into IMFs having the same spectral shape but that are shifted in the frequency domain.…”

Section: Adaptive Background Null Hypothesismentioning

confidence: 99%

On the intrinsic timescales of temporal variability in measurements of the surface solar radiation

Bengulescu

Blanc

Wald

2018

Nonlin. Processes Geophys.

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Abstract. This study is concerned with the intrinsic temporal scales of the variability in the surface solar irradiance (SSI). The data consist of decennial time series of daily means of the SSI obtained from high-quality measurements of the broadband solar radiation impinging on a horizontal plane at ground level, issued from different Baseline Surface Radiation Network (BSRN) ground stations around the world. First, embedded oscillations sorted in terms of increasing timescales of the data are extracted by empirical mode decomposition (EMD). Next, Hilbert spectral analysis is applied to obtain an amplitude-modulation-frequencymodulation (AM-FM) representation of the data. The timevarying nature of the characteristic timescales of variability, along with the variations in the signal intensity, are thus revealed. A novel, adaptive null hypothesis based on the general statistical characteristics of noise is employed in order to discriminate between the different features of the data, those that have a deterministic origin and those being realizations of various stochastic processes. The data have a significant spectral peak corresponding to the yearly variability cycle and feature quasi-stochastic high-frequency variability components, irrespective of the geographical location or of the local climate. Moreover, the amplitude of this latter feature is shown to be modulated by variations in the yearly cycle, which is indicative of nonlinear multiplicative cross-scale couplings. The study has possible implications on the modeling and the forecast of the surface solar radiation, by clearly discriminating the deterministic from the quasistochastic character of the data, at different local timescales.

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“…The influence of the signal length on the number of the IMFs and their statistics has been investigated in [19,20] on the basis of extensive simulations. For the corpora used in the experiment, the number of IMFs per speech frame log spectrum varies between 8 and 12.…”

Section: Empirical Mode Decomposition Algorithmmentioning

confidence: 99%