Signal decomposition by the S-method with general window functions

Yan, Wei; Tan, Shanshan

doi:10.1016/j.sigpro.2011.06.013

Cited by 7 publications

(6 citation statements)

References 6 publications

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“…Decomposition of non-stationary multicomponent signals has been a long-term, challenging topic in time-frequency signal analysis [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Although decomposition of nonoverlapping components can be done using the S-method relations with the WD [26], this approach cannot be applied when the components partially overlap, i.e., share the same domain of support in the time-frequency plane.…”

Section: Discussionmentioning

confidence: 99%

“…In order to characterize multicomponent signals, it is quite common to perform signal decomposition, which assumes that each individual component is extracted for separate analysis, such as for the IF estimation. Decomposition techniques for multicomponent signals are quite efficient if components do not overlap in the time-frequency plane [19][20][21][22][23][24][25][26]. The method originally presented in [26] can be used to completely extract each component by using an intrinsic relation between the PWD and the SM.…”

Section: Introductionmentioning

confidence: 99%

“…The method originally presented in [26] can be used to completely extract each component by using an intrinsic relation between the PWD and the SM. In the analysis of multicomponent signals, it is, however, common that various components partially overlap in the time-frequency plane, making the decomposition process particularly challenging [19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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Multivariate Decomposition of Acoustic Signals in Dispersive Channels

et al. 2021

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We present a signal decomposition procedure, which separates modes into individual components while preserving their integrity, in effort to tackle the challenges related to the characterization of modes in an acoustic dispersive environment. With this approach, each mode can be analyzed and processed individually, which carries opportunities for new insights into their characterization possibilities. The proposed methodology is based on the eigenanalysis of the autocorrelation matrix of the analyzed signal. When eigenvectors of this matrix are properly linearly combined, each signal component can be separately reconstructed. A proper linear combination is determined based on the minimization of concentration measures calculated exploiting time-frequency representations. In this paper, we engage a steepest-descent-like algorithm for the minimization process. Numerical results support the theory and indicate the applicability of the proposed methodology in the decomposition of acoustic signals in dispersive channels.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multivariate Decomposition of Acoustic Signals in Dispersive Channels

et al. 2021

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“…The authors of [32] present a signal decomposition method by the SM with general window functions to decompose wideband LFM signals. Similarly, we can modify the proposed detector by adding a general window function in the calculation of the CSM.…”

Section: Discussionmentioning

confidence: 99%

CFAR Detection of Range-Spread Targets Based on the Time-Frequency Decomposition Feature of Two Adjacent Returned Signals

Zuo

Zhang

et al. 2013

IEEE Trans. Signal Process.

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Radar returned signals are processed by stretch processing, resulting in mixer outputs. Based on the time-frequency decomposition of the cross S-method (CSM) of two adjacent mixer outputs, a range-spread target detector is proposed in this paper. As a preparatory work, we propose a signal synthesis method (SSM) based on the singular value decomposition. The SSM synthesizes two signals in their normalized forms from their cross Wigner distribution (CWD) and concentrates their energy on two singular values. This detector consists of three steps. First, we derive the CSM from the S-method (SM). The CSM is close to the sum of the CWDs of the components in one mixer output and their counterparts in the other. Second, we can decompose the CSM by the SSM, thereby obtaining singular values. Third, the time-frequency decomposition feature, i.e., the ratio of the sum of several biggest singular values to the median or mean of the rest, is defined to demonstrate the concentration of the singular values and used to detect the range-spread target. The proposed detector is evaluated by the raw radar data without range migration correction. Results show that it outperforms the conventional detectors. In addition, we prove that the proposed detector has the constant false-alarm rate (CFAR) property.Index Terms-Cross S-method (CSM), constant false-alarm rate (CFAR), range-spread target detector, signal decomposition, singular values.

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“…For an independent characterization, each signal (component) in a multicomponent signal should be separated from others and individually analyzed [4,5,6,7]. Such decomposition of multicomponent signals on individual components is possible for univariate signals by means of the algorithm originally presented in [4], which is based on the S-method.…”

Section: Introductionmentioning

confidence: 99%