Multifractal analysis based on amplitude extrema of intrinsic mode functions

Welter, Guilherme Sausen; Esquef, Paulo A. A.

doi:10.1103/physreve.87.032916

Cited by 19 publications

(34 citation statements)

References 56 publications

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“…On the one hand, an infinite number of sifting iterations would asymptotically approach the result of the Fourier decomposition (i.e., constant amplitude envelopes) (Wang et al, 2010). On the other hand, several studies performed on time series of pure noise Flandrin et al, 2004a;Wu and Huang, 2004) have shown the decomposition behaves like an adaptive "wavelet-like" dyadic filter if the number of sifting iterations is kept small, around 10, which also assures maximum component separation and minimum leakage . This stoppage criterion of 10 sifting iterations is currently the recommended one for practical applications Huang, 2009, 2010) and is also the one employed in the study.…”

Section: The Empirical Mode Decompositionmentioning

confidence: 99%

“…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%

“…In Sect. 5.1, evidence is presented that the spectral band spanning from 2 to 300 days seems to be composed mostly of random realizations of stochastic background processes, which can be modeled following, e.g., Flandrin et al (2004a), Rilling et al (2005), Welter and Esquef (2013), and Kolotkov et al (2016).…”

Section: The Intrinsic Timescales Of Variability In the Ssimentioning

confidence: 99%

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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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Section: The Empirical Mode Decompositionmentioning

confidence: 99%

Section: Adaptive Background Null Hypothesismentioning

confidence: 99%

Section: The Intrinsic Timescales Of Variability In the Ssimentioning

confidence: 99%

See 1 more Smart Citation

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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show abstract

Section: The Empirical Mode Decompositionmentioning

confidence: 99%

Answer to Tommaso Alberti

Wald¹

2017

View full text Add to dashboard Cite

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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“…(For review and comparison of distinct methods c.f. [39,45].) In this study a recently proposed formalism [39], which is briefly described in the sequel, is employed for analysis.…”

Section: Multifractal Analysismentioning

confidence: 99%

Multifractality in fidelity sequences of optimized Toffoli gates

Moqadam

Welter

Esquef

2016

Quantum Inf Process

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We analyze the multifractality of the fidelity in an engineered Toffoli gate. Using quantum control methods, we define several optimization problems whose global solutions realize the gate in a chain of three qubits with XY Heisenberg interaction. We perturb the system by introducing imperfections in the form of 1/f noise to the interqubit couplings. Multifractal analysis shows that the degree of multifractality in the gate fidelity increases when optimized control pulses used to render the fidelity are less sensitive to variations in the interqubits coupling strengths.

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Multifractal analysis based on amplitude extrema of intrinsic mode functions

Cited by 19 publications

References 56 publications

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

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

Answer to Tommaso Alberti

Multifractality in fidelity sequences of optimized Toffoli gates

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