Recent Mathematical Developments on Empirical Mode Decomposition

Xu, Yuesheng; Zhang, Haizhang

doi:10.1142/s1793536909000242

Cited by 14 publications

(10 citation statements)

References 35 publications

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“…The derivative must be well defined, as physically there can only be one instantaneous frequency value f(t) at a given time t. This is ensured by the narrow band condition: the signal must contain nearly one frequency. Furthermore, as detailed by Xu and Zhang [60], the HT produces a more physically meaningful result the closer its input signal is to being narrow band. The EMD combined with HAS provides time-frequency-amplitude representation of the original data generated from non-linear non-stationary and stochastic processes, and the spectrum is called the Hilbert-Huang spectrum (HHT).…”

Section: Empirical Mode Decomposition (Emd)mentioning

confidence: 92%

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Speaker Verification Under Degraded Conditions Using Empirical Mode Decomposition Based Voice Activity Detection Algorithm

Rudramurthy

Prasad

Kumaraswamy

2014

Journal of Intelligent Systems

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The performance of most of the state-of-the-art speaker recognition (SR) systems deteriorates under degraded conditions, owing to mismatch between the training and testing sessions. This study focuses on the front end of the speaker verification (SV) system to reduce the mismatch between training and testing. An adaptive voice activity detection (VAD) algorithm using zero-frequency filter assisted peaking resonator (ZFFPR) was integrated into the front end of the SV system. The performance of this proposed SV system was studied under degraded conditions with 50 selected speakers from the NIST 2003 database. The degraded condition was simulated by adding different types of noises to the original speech utterances. The different types of noises were chosen from the NOISEX-92 database to simulate degraded conditions at signal-to-noise ratio levels from 0 to 20 dB. In this study, widely used 39-dimension Mel frequency cepstral coefficient (MFCC; i.e., 13-dimension MFCCs augmented with 13-dimension velocity and 13-dimension acceleration coefficients) features were used, and Gaussian mixture model-universal background model was used for speaker modeling. The proposed system's performance was studied against the energy-based VAD used as the front end of the SV system. The proposed SV system showed some encouraging results when EMD-based VAD was used at its front end.Keywords: Voice activity detection (VAD), zero-frequency filter assisted peaking resonator (ZFFPR), empirical mode decomposition (EMD), speaker verification (SV), Gaussian mixture model-universal background model (GMM-UBM).

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Section: Empirical Mode Decomposition (Emd)mentioning

confidence: 92%

“…More details on the statistical significance of the IMFs obtained through EMD are described in Refs. [20,59,60]. Like any other methods, EMD has one major limitation: mode mixing.…”

Section: Empirical Mode Decomposition (Emd)mentioning

confidence: 99%

Speaker Verification Under Degraded Conditions Using Empirical Mode Decomposition Based Voice Activity Detection Algorithm

Rudramurthy

Prasad

Kumaraswamy

2014

Journal of Intelligent Systems

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“…The great success of empirical mode decomposition in the signal analysis has stimulated considerable attention to the time‐frequency analysis from the mathematics community. Especially, the important Bedrosian identity has been extensively studied . So far, most studies have been focused on the continuous case, namely, the functions considered therein live in

L^{2} (double-struckR)

.…”

Section: Introductionmentioning

confidence: 99%

The circular Bedrosian identity for translation‐invariant operators: existence and characterization

Lin

Zhang

2015

Math Methods in App Sciences

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Communicated by T. QianThe analytic signal method via the circular Hilbert transform Q H is a critical tool in the time-frequency analysis of signals of finite duration. The circular Bedrosian identity Q H.fg/ D f Q Hg is of major theoretical and practical value in the method. The identity holds whenever the Fourier coefficients of f, g 2 L 2 .OE , / are respectively supported on A D OE n, m and B D Z n OE m, n for some non-negative integers 0 Ä n, m Ä C1. In this note, we investigate the existence of such an identity for a general-bounded linear translation-invariant operator on L 2 .OE , d / and for general support sets A, B Â Z d . We give an insightful geometric characterization of the support sets for the existence. In addition, we find all the support sets for the partial Hilbert transforms.

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“…It is desirable to build a solid mathematical base for the algorithm. There are two stages in building such a base for the useful algorithm, [21]. The first is to construct a large bank M of functions f ∈ L 2 r (R) such that…”

Section: Introductionmentioning

confidence: 99%

Orthonormal bases with nonlinear phases

Qian

Wang

et al. 2009

Adv Comput Math

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For adaptive representation of nonlinear signals, the bank M of real square integrable functions that have nonlinear phases and nonnegative instantaneous frequencies under the analytic signal method is investigated. A particular class of functions with explicit expressions in M is obtained using Communicated by Qiyu Sun. 76 T. Qian et al.recent results on the Bedrosian identity. We then construct orthonormal bases for the Hilbert space of real square integrable functions with the basis functions from M.

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Recent Mathematical Developments on Empirical Mode Decomposition

Cited by 14 publications

References 35 publications

Speaker Verification Under Degraded Conditions Using Empirical Mode Decomposition Based Voice Activity Detection Algorithm

Speaker Verification Under Degraded Conditions Using Empirical Mode Decomposition Based Voice Activity Detection Algorithm

The circular Bedrosian identity for translation‐invariant operators: existence and characterization

Orthonormal bases with nonlinear phases

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