A signal decomposition theorem with Hilbert transform and its application to narrowband time series with closely spaced frequency components

Chen, Genda; Wang, Zuo‐Cai

doi:10.1016/j.ymssp.2011.02.002

Cited by 157 publications

(87 citation statements)

References 14 publications

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“…Clearly, for different instantaneous frequencies (the constant frequency, the linear modulation frequency and the quadratic modulation frequency), the decompositions are the similar and we can obtain the same result: if the amplitude a and the frequency ratio k are in the blue regions, i.e., the middle region between the two functions The example in Figure 1 is a breakthrough of the decomposition theorem in [16]. The simulations in Figures 2 and 3 verify that this breakthrough is rational and find the performance bounds for the separation of two AM-FM components.…”

Section: The Conditions For Hypothesissupporting

confidence: 52%

“…The decomposition theorem [16] by G. Chen and Z. Wang is defined as follows. Let ( ) x t denote a real time series of n significant frequency components ( 1 2 , , , 0 The proof of this theorem can be found in [2].…”

Section: Component Separationmentioning

confidence: 99%

“…The compared methods include the empirical mode decomposition (EMD) [12], the improved EMD (IEMD) [2], the Hilbert transform based method [16] via Fourier spectra, the masking method [13,14] and our proposed method. In EMD we will use the most related IMF to the original true component as the according separated component.…”

Section: On Simulationsmentioning

confidence: 99%

“…On the other hand, the second task-the decomposition of multi-components is also an important problem in signal processing. The adaptive methods for signal separation should be explored [2,[8][9][10][11][12][13][14][15][16][17][18] especially for the separation of multiple components blended in noise data. That is to say, the separation of signals from real-life observed noisy data includes two steps' work, filtering the signals and then decomposing the signals to multiple independent components.…”

Section: Introductionmentioning

confidence: 99%

“…There have been some methods involving decomposing the superposed AM-FM components, including the frequency domain separation method such as the LFM (linear frequency modulation) component separation via FRFT [17], the empirical mode decomposition (EMD) [3,12], the improved EMD (IEMD) [2,8] (the method in [8] is only for pure FM signal), the masking method [13,14] and the Hilbert transform [1,19] based method [16]. The frequency domain separation method is the most traditional method to separate the superposed AM-FM components in frequency domain or fractional frequency domain [17] through finding the separation points or peak points.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Time-Varying Bandpass Filter Based on Assisted Signals for AM-FM Signal Separation: A Revisit

Gao¹,

Wang²,

Xu³

et al. 2013

JSIP

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In this paper, a new signal separation method mainly for AM-FM components blended in noises is revisited based on the new derived time-varying bandpass filter (TVBF), which can separate the AM-FM components whose frequencies have overlapped regions in Fourier transform domain and even have crossed points in time-frequency distribution (TFD) so that the proposed TVBF seems like a "soft-cutter" that cuts the frequency domain to snaky slices with rational physical sense. First, the Hilbert transform based decomposition is analyzed for the analysis of nonstationary signals. Based on the above analysis, a hypothesis under a certain condition that AM-FM components can be separated successfully based on Hilbert transform and the assisted signal is developed, which is supported by representative experiments and theoretical performance analyses on a error bound that is shown to be proportional to the product of frequency width and noise variance. The assisted signals are derived from the refined time-frequency distributions via image fusion and least squares optimization. Experiments on man-made and real-life data verify the efficiency of the proposed method and demonstrate the advantages over the other main methods.

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Section: The Conditions For Hypothesissupporting

confidence: 52%

Section: Component Separationmentioning

confidence: 99%

Section: On Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Time-Varying Bandpass Filter Based on Assisted Signals for AM-FM Signal Separation: A Revisit

Gao¹,

Wang²,

Xu³

et al. 2013

JSIP

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A time frequency domain digital implementation of flickermeter using analytical mode decomposition

Tian

Zhu³

et al. 2019

Int Trans Electr Energ Syst

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Summary Flickers of wind farm should be assessed accurately since they become a limiting factor for integrating wind turbines into grid. Furthermore, since cyclical low‐frequency oscillation powers (CLFOPs) caused by wind turbines will lead to low‐frequency oscillation in the power system, CLFOP monitor and mitigation is wanted. A novel digital time‐frequency domain implementation of flickermeter using analytical mode decomposition (AMD) is proposed in this paper. The results of simulation and actual measurement show the proposed flickermeter can (1) meet design standard requirements of IEC 61000‐4‐15; (2) obtain the more accurate CLFOP monitor in time‐frequency domain compared with wavelet packet decomposition (WPD) and empirical mode decomposition (EMD); and (3) realize the CLFOP mitigation for reducing the probability of low‐frequency oscillation in power system through sending the power limitation instruction to the energy management system (EMS) of wind farm.

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Response-only modal identification of structures using limited sensors

Abazarsa

Ghahari

Nateghi

et al. 2012

Struct. Control Health Monit.

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Herein, we propose a method based on the existing second-order blind identification of underdetermined mixtures technique for identifying the modal characteristics-namely, natural frequencies, damping ratio, and real-valued partial mode shapes of all contributing modes-of structures with a limited number of sensors from recorded free/ ambient vibration data. In the second-order blind identification approach, second-order statistics of recorded signals are used to recover modal coordinates and mode shapes. Conventional versions of this approach require the number of sensors to be equal to or greater than the number of active modes. In the present study, we first employ a parallel factor technique to decompose the covariance tensor into rank-one tensors so that the partial mode shapes at the recording locations (sensors) can be estimated. The mode shape matrix identified in this manner is not square, which precludes the use of a simple inversion to extract the modal coordinates. As such, the natural frequencies are identified from the recovered modal coordinates' Autocovariances. The damping ratios are extracted using a least-squares technique from modal free vibrations, as they are not directly recoverable because of the inherent smearing produced by windowing processes. Finally, a Bayesian model updating approach is employed to complete the partial mode shapes-that is, to extract the mode shapes at the DOFs without sensors. We use simulated and physical data for verifying and validating this new identification method, and explore optimal sensor distribution in multistory structures for a given (limited) number of sensors. particular extraction method works without having the sources or the mixing processes-hence, the term blind-and employs second-order statistics of recorded response signals to recover the modal coordinate signals and the mode shape matrix. However, SOBI method does not work well in the presence of highly damped, low-energy or closely spaced modes, severe nonstationary excitations, and relatively large measurement noise. The issues of weakly nonstationary signals and noisy measurement were addressed in [20], whereas separability of low-energy modes was improved by employing stationary wavelet transform in [21]. Nevertheless, conventional versions of SOBI methods are limited to determined or overdetermined problems, in which the number of active modes is equal to or less than the number of recorded signals. For civil structures (e.g., tall buildings, long-span bridges, etc.), this constraint is often prohibitive.Various algorithms are presented in the signal processing literature for underdetermined problems, and in most such studies, the source signals (here, the modal coordinates) are assumed to be sparse [22,23]. Given this condition, time-frequency representations along with clustering techniques [24,25] or modal decompositions [26] are used to identify the source signals. Nevertheless, aforementioned methods are not suitable for modal identification of civil structures because their free or a...

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A signal decomposition theorem with Hilbert transform and its application to narrowband time series with closely spaced frequency components

Cited by 157 publications

References 14 publications

Time-Varying Bandpass Filter Based on Assisted Signals for AM-FM Signal Separation: A Revisit

Time-Varying Bandpass Filter Based on Assisted Signals for AM-FM Signal Separation: A Revisit

A time frequency domain digital implementation of flickermeter using analytical mode decomposition

Response-only modal identification of structures using limited sensors

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