Analysis and synthesis of multicomponent signals using positive time-frequency distributions

Francos, A.; Porat, Moshe

doi:10.1109/78.740132

Cited by 59 publications

(41 citation statements)

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“…The initial phase ϕ 0 = Φ[0] is referenced to the time-window center to minimize the estimation error [19]; ϕ 0 is not set to zero contrary to all literature examples [7][8][9][10][11][12][13][14][15]. We assume…”

Section: Polynomial Amplitude and Frequency Modelmentioning

confidence: 99%

“…The instantaneous amplitude and frequency of the signals are frequently presented as time-varying functions [7][8][9][10][11][12][13][14][15] where polynomial function models have been assigned to the signal phase. In [12], Francos and Porat's algorithm combined a time-frequency distribution of a minimum-cross-entropy with the Higher Ambiguity Function (HAF) [7] to achieve the model parameter estimation.…”

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confidence: 99%

“…In [12], Francos and Porat's algorithm combined a time-frequency distribution of a minimum-cross-entropy with the Higher Ambiguity Function (HAF) [7] to achieve the model parameter estimation. The HAF technique, which is a suboptimal compared to the maximum likelihood procedure, transforms a signal of a M Despite its low computational complexity, the robustness of the HAF technique is considerably limited by the lag choice and the propagation error phenomenon [15] which occurs in the presence of a higher-order polynomial modeling and/or a strong noise.…”

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confidence: 99%

“…The HAF technique, which is a suboptimal compared to the maximum likelihood procedure, transforms a signal of a M Despite its low computational complexity, the robustness of the HAF technique is considerably limited by the lag choice and the propagation error phenomenon [15] which occurs in the presence of a higher-order polynomial modeling and/or a strong noise. Consequently, the Francos and Porat's algorithm [12] fails at low Signal to Noise Ratios (SNRs) and high model orders.…”

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confidence: 99%

“…First, the model origin and the initial phase are referenced at the center of the time window. Then, contrary to [7][8][9][10][11][12][13][14][15], the instantaneous frequency instead of the phase is approximated by a discrete polynomial function. We compare different polynomial bases and we…”

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confidence: 99%

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Estimation of the instantaneous amplitude and frequency of non-stationary short-time signals

et al. 2008

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We consider the modeling of non-stationary discrete signals whose amplitude and frequency are assumed to be nonlinearly modulated over very short-time duration.We investigate the case where both instantaneous amplitude and frequency can be approximated by orthonormal polynomials.Previous works dealing with polynomial approximations refer to orthonormal bases built from a discretization of continuous-time orthonormal polynomials. As this leads to a loss of the orthonormal property, we propose to use discrete orthonormal polynomial bases: the discrete orthonormal Legendre polynomials and a discrete base we have derived using Gram-Schmidt procedure. We show that in the context of short-time signals the use of these discrete bases leads to a significant improvement in the estimation accuracy. we propose to apply a stochastic optimization technique based on the simulated annealing algorithm. The problem can also be considered as a Bayesian estimation which leads us to apply another stochastic technique based on Monte Carlo MarkovChains. We propose to use a Metropolis Hastings algorithm. Both approaches need an algorithm parameter tuning that we discuss according our application context.Monte Carlo simulations show that the results obtained are close to the CramerRao bounds we have derived. We show that the first approach is less biased than the second one. We also compared our results with the Higher Ambiguity Functionbased method. The methods proposed outperform this method at low signal to noise ratios in terms of estimation accuracy and robustness. Both proposed approaches are of a great utility when scenarios in which signals having a small sample size are nonstationary at low signal to noise ratios. They provide accurate system descriptions which are achieved with only a reduced number of basis functions.

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Section: Polynomial Amplitude and Frequency Modelmentioning

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Estimation of the instantaneous amplitude and frequency of non-stationary short-time signals

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Estimation of Multiple Periodic Motions from Video

Briassouli

Ahuja

2006

Computer Vision – ECCV 2006

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Abstract. The analysis of periodic or repetitive motions is useful in many applications, both in the natural and the man-made world. An important example is the recognition of human and animal activities. Existing methods for the analysis of periodic motions first extract motion trajectories, e.g. via correlation, or feature point matching. We present a new approach, which takes advantage of both the frequency and spatial information of the video. The 2D spatial Fourier transform is applied to each frame, and time-frequency distributions are then used to estimate the time-varying object motions. Thus, multiple periodic trajectories are extracted and their periods are estimated. The period information is finally used to segment the periodically moving objects. Unlike existing methods, our approach estimates multiple periodicities simultaneously, it is robust to deviations from strictly periodic motion, and estimates periodicities superposed on translations. Experiments with synthetic and real sequences display the capabilities and limitations of this approach. Supplementary material is provided, showing the video sequences used in the experiments.

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Mono-component AM–FM Signal Decomposition Based on Discrete Second-Order Generalized Integrator Phase-Locked Loop

George

Sumathi

2016

Circuits Syst Signal Process

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Analysis and synthesis of multicomponent signals using positive time-frequency distributions

Cited by 59 publications

References 15 publications

Estimation of the instantaneous amplitude and frequency of non-stationary short-time signals

Estimation of the instantaneous amplitude and frequency of non-stationary short-time signals

Estimation of Multiple Periodic Motions from Video

Mono-component AM–FM Signal Decomposition Based on Discrete Second-Order Generalized Integrator Phase-Locked Loop

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