Estimation of amplitude and phase parameters of multicomponent signals

Friedlander, B.; Francos, J.M.

doi:10.1109/78.376844

Cited by 137 publications

(106 citation statements)

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“…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%

“…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%

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

et al. 2008

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“…As the CRB is the lower bound on the estimation accuracy of an unbiased estimator, estimation errors are not directly comparable with the CRBs given in [4][5][6]. Here, it is just used as a reference in evaluating the performance of the algorithms.…”

Section: Base Effectsmentioning

confidence: 99%

“…P and Q are polynomial orders of the amplitude and the phase respectively. In [4], Friedlander and Francos derived the CRB for polynomial amplitude and phase for the entire modulation.…”

Section: Cramer Rao Boundmentioning

confidence: 99%

“…In Section III, we develop the time segmentation algorithm. In Section IV, Cramer Rao bounds (CRB) derived in [4] for the entire frequency and amplitude are compared to the proposed global estimator. The analysis of numerical simulations and a real signal are discussed in Section V. Finally Section VI sets out our conclusions and work in progress.…”

Section: Introduction and Outlinementioning

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