Multicomponent signal analysis using the polynomial-phase transform

Peleg, Shir; Friedlander, B.

doi:10.1109/7.481277

Cited by 127 publications

(89 citation statements)

References 11 publications

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“…Its residual content will be highly localized around the 0 Hz spectral region [12,13]. It is able to efficiently remove this component via Step 3 [14].…”

Section: Limitations Of Pgcpfmentioning

confidence: 99%

An Efficient Algorithm for Estimating the Parameters of Multicomponent Cubic Phase Signals

Tang¹,

Yuan²,

Lin³

et al. 2013

Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013)

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“…Its residual content will be highly localized around the 0 Hz spectral region [12,13]. It is able to efficiently remove this component via Step 3 [14].…”

Section: Limitations Of Pgcpfmentioning

confidence: 99%

An Efficient Algorithm for Estimating the Parameters of Multicomponent Cubic Phase Signals

Tang¹,

Yuan²,

Lin³

et al. 2013

Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013)

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“…However, in many practical situations that we have dealt with, components belonging to the same signal source do not generally intersect (e.g., newborn EEG seizure signal analysis [1]), so we have chosen to apply our modifications to the second algorithm only. Furthermore, the chosen algorithm, unlike some other algorithms for estimation of multicomponent signals in noise (e.g., [34][35][36]) is not limited to the polynomial phase signals and can also be used in estimation of other nonlinear phase signals, as most real-life signals are (e.g., the echolocation sound emitted by a bat, used in this paper). The components are extracted one by one, until the remaining energy of the TFD becomes sufficiently small [37].…”

Section: Algorithm For Signal Components Extractionmentioning

confidence: 99%

An Efficient Algorithm for Instantaneous Frequency Estimation of Nonstationary Multicomponent Signals in Low SNR

Lerga

Sucic

Boashash

2011

EURASIP J. Adv. Signal Process.

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A method for components instantaneous frequency (IF) estimation of multicomponent signals in low signal-to-noise ratio (SNR) is proposed. The method combines a new proposed modification of a blind source separation (BSS) algorithm for components separation, with the improved adaptive IF estimation procedure based on the modified sliding pairwise intersection of confidence intervals (ICI) rule. The obtained results are compared to the multicomponent signal ICI-based IF estimation method for various window types and SNRs, showing the estimation accuracy improvement in terms of the mean squared error (MSE) by up to 23%. Furthermore, the highest improvement is achieved for low SNRs values, when many of the existing methods fail. Signal Model and Problem FormulationMany signals in practice, such as those found in speech processing, biomedical applications, seismology, machine condition monitoring, radar, sonar, telecommunication, and many other applications are nonstationary [1]. Those signals can be categorized as either monocomponent or multicomponent signals, where the monocomponent signal, unlike the multicomponent one, is characterized in the timefrequency domain by a single "ridge" corresponding to an elongated region of energy concentration [1].For a real signal s(t), its analytic equivalent z(t) is defined aswhere H {s(t)} is the Hilbert transformation of s(t), a(t) is the signal instantaneous amplitude, and φ(t) is the signal instantaneous phase. The instantaneous frequency (IF) describes the variations of the signal frequency contents with time; in the case of a frequency-modulated (FM) signal, the IF represents the FM modulation law and is often referred to as simply the IF law [2,3]. The IF of the monocomponent signal z(t) is the first derivative of its instantaneous phase, that is, ω(t) = φ (t) [1]. Furthermore, the crest of the "ridge" is often used to estimate the IF of the signal z(t) as [1]whereOn the other hand, the analytical multicomponent signal x(t) can be modeled as a sum of two or more monocomponent signals (each with its own IF ω m (t))where M is the number of signal components, a m (t) is the mth component instantaneous amplitude, and φ m (t) is its instantaneous phase. When calculating the Hilbert transform of the signal s(t) in (1), the conditions of Bedrosian's theorem need to be satisfied, that is, a(t) has to be a low frequency function with the spectrum which does not overlap with the e jφ(t) spectrum [2-5].

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“…Case 2) The value of is unknown. For this case, we estimate the value of by the discrete polynomial-phase transform (DPT) method [22], [23]. The estimation precision can be further improved by searching with a finer step size within a limited range around the estimated value of .…”

Section: ) Selection Ofmentioning

confidence: 99%

Sparse Discrete Fractional Fourier Transform and Its Applications

Liu¹,

Shan²,

Tao³

et al. 2014

IEEE Trans. Signal Process.

135

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Abstract-The discrete fractional Fourier transform is a powerful signal processing tool with broad applications for nonstationary signals. In this paper, we propose a sparse discrete fractional Fourier transform (SDFrFT) algorithm to reduce the computational complexity when dealing with large data sets that are sparsely represented in the fractional Fourier domain. The proposed technique achieves multicomponent resolution in addition to its low computational complexity and robustness against noise. In addition, we apply the SDFrFT to the synchronization of high dynamic direct-sequence spread-spectrum signals. Furthermore, a sparse fractional cross ambiguity function (SFrCAF) is developed, and the application of SFrCAF to a passive coherent location system is presented. The experiment results confirm that the proposed approach can substantially reduce the computation complexity without degrading the precision.Index Terms-Cross ambiguity function, global positioning system, passive bistatic radar, sparse discrete fractional Fourier transform.

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Multicomponent signal analysis using the polynomial-phase transform

Cited by 127 publications

References 11 publications

An Efficient Algorithm for Estimating the Parameters of Multicomponent Cubic Phase Signals

An Efficient Algorithm for Estimating the Parameters of Multicomponent Cubic Phase Signals

An Efficient Algorithm for Instantaneous Frequency Estimation of Nonstationary Multicomponent Signals in Low SNR

Sparse Discrete Fractional Fourier Transform and Its Applications

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