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Estimation of Frequency for AM/FM Models Using the Phase Vocoder Framework
 IEEE Transactions on Signal Processing
, 2008
"... Abstract—This paper proposes an extension of the applicability of phasevocoderbased frequency estimators for generalized sinusoidal models, which include phase and amplitude modulations. A first approach, called phase corrected vocoder (PCV), takes into account the modification of the Fourier phas ..."
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Abstract—This paper proposes an extension of the applicability of phasevocoderbased frequency estimators for generalized sinusoidal models, which include phase and amplitude modulations. A first approach, called phase corrected vocoder (PCV), takes into account the modification of the Fourier phases resulting from these modulations. Another approach is based on an adaptation of the principles of the timefrequency reassignment and is referred to as the reassigned vocoder (RV). The robustness of the estimation against noise is studied, both theoretically and experimentally, and the performance is assessed in comparison with two stateoftheart algorithms: an unmodified version of the reassignment method and a quadratically interpolated fast Fourier transform method (QIFFT). Index Terms—AM/FM model, frequency estimation, phase vocoder. I.
A AM/FM Single Component Signal Reconstruction using a Nonsequential Time Segmentation and Polynomial Modeling
"... Abstract — The problem of estimating nonstationary signals has been considered in many previous publications. In this paper we propose an alternative algorithm in order to accurately estimate AM/FM 1 signals. Only single component signals are considered. We perform local polynomial modeling on short ..."
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Abstract — The problem of estimating nonstationary signals has been considered in many previous publications. In this paper we propose an alternative algorithm in order to accurately estimate AM/FM 1 signals. Only single component signals are considered. We perform local polynomial modeling on short time segments using a nonsequential strategy. The degree of polynomial approximation is limited due to the shortness of each time segment. The time support of a segment is controlled by a criterion defined on the spectrogram. To keep optimality a maximum likelihood procedure estimates the local model parameters leading to a non linear equation system in R 7. This is solved by a Simulated Annealing technique. Finally, the local polynomial models are merged to reconstruct the entire signal model. The proposed algorithm enables highly nonlinear AM/FM estimation and shows robustness even when Signal to Noise Ratio (SNR) is low. The appropriate Cramer Rao Bounds (CRB) are presented for both polynomial phase and amplitude signals. Monte Carlo simulations show that the proposed algorithm performs well. Finally, our proposed method is illustrated using both numerical simulations and a real signal of whale sound. I. INTRODUCTION AND OUTLINE This paper is concerned with the commonly encountered problem of estimating nonlinear AM/FM signals. This topic is frequently addressed in engineering systems and applied
A Generalization of the Fourier Transform and its Application to Spectral Analysis of Chirplike Signals
, 2011
"... We show that the de Branges theory provides a useful generalization of the Fourier Transform (FT). The formulation is quite rich in that by selecting the appropriate parametrization, one can obtain spectral representation for a number of important cases. We demonstrate two such cases in this paper: ..."
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We show that the de Branges theory provides a useful generalization of the Fourier Transform (FT). The formulation is quite rich in that by selecting the appropriate parametrization, one can obtain spectral representation for a number of important cases. We demonstrate two such cases in this paper: the finite sum of elementary chirplike signals, and a decaying chirp using Bessel functions. We show that when defined in the framework of de Branges spaces, these cases admit a representation very much similar to the spectral representation of a finite sum of sinusoids for the usual FT.
Estimation of the Instantaneous Amplitude and Frequency of Nonstationary Shorttime Signals
, 2007
"... We consider the modeling of nonstationary discrete signals whose amplitude and frequency are assumed to be nonlinearly modulated over very shorttime duration. We investigate the case where both instantaneous amplitude and frequency can be approximated by orthonormal polynomials. Previous works dea ..."
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We consider the modeling of nonstationary discrete signals whose amplitude and frequency are assumed to be nonlinearly modulated over very shorttime 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 continuoustime 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 GramSchmidt procedure. We show that in the context of shorttime signals the use of these discrete bases leads to a significant improvement in the estimation accuracy. We manage the model parameter estimation by applying two approaches. The first is maximization of the likelihood function. This function being highly nonlinear, Preprint submitted to Elsevier Science 21 September 2007we 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 Markov Chains. 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 non
Parameter estimation of chirp signals in presence of stationary noise, Statistica Sinica 18
, 2008
"... Abstract. The problem of parameter estimation of the chirp signals in presence of stationary noise has been addressed. We consider the least squares estimators and it is observed that the least squares estimators are strongly consistent. The asymptotic distributions of the least squares estimators ..."
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Abstract. The problem of parameter estimation of the chirp signals in presence of stationary noise has been addressed. We consider the least squares estimators and it is observed that the least squares estimators are strongly consistent. The asymptotic distributions of the least squares estimators are obtained. The multiple chirp signal model is also considered and we obtain the asymptotic properties of the least squares estimators of the unknown parameters. We perform some small sample simulations to observe how the proposed estimators work for small sample sizes. 1.
FREQUENCY SLOPE ESTIMATION AND ITS APPLICATION FOR NONSTATIONARY SINUSOIDAL PARAMETER ESTIMATION
"... In the following paper we investigate into the estimation of sinusoidal parameters for sinusoids with linear AM/FM modulation. It will be shown that for linear amplitude and frequency modulation only the frequency modulation creates additional estimation bias for the standard sinusoidal parameter es ..."
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In the following paper we investigate into the estimation of sinusoidal parameters for sinusoids with linear AM/FM modulation. It will be shown that for linear amplitude and frequency modulation only the frequency modulation creates additional estimation bias for the standard sinusoidal parameter estimator. Then an enhanced algorithm for frequency domain demodulation of spectral peaks is proposed that can be used to obtain an approximate maximum likelihood estimate of the frequency slope, and an estimate of the amplitude, phase and frequency parameter with significantly reduced bias. An experimental evaluation compares the new estimation scheme with previously existing methods. It shows that significant bias reduction is achieved for a large range of slopes and zero padding factors. A real world example demonstrates that the enhanced bias reduction algorithm can achieve a reduction of the residual energy of up to 9dB. 1.