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13
Multicomponent Polynomial Phase Signal Analysis Using a Tracking Algorithm
, 1999
"... We describe an efficient technique analyzing signals that comprise a number of polynomial phase components. The technique is based on a recently proposed "multiple frequency tracker", an algorithm for recursive estimation of parameters of multiple sine waves in noise. It has a relatively low SNR thr ..."
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We describe an efficient technique analyzing signals that comprise a number of polynomial phase components. The technique is based on a recently proposed "multiple frequency tracker", an algorithm for recursive estimation of parameters of multiple sine waves in noise. It has a relatively low SNR threshold and moderate computational complexity. 1 Introduction Polynomial phase signals are encountered for example in pulse compression radar systems, [1], in synthetic aperture radar imaging and mobile communications, [2], or in modeling certain animal sounds, [1]. For these applications, signals with a quadratic and cubic polynomial phase, i.e. linear and quadratic frequency modulated (FM) signals, are the most important. For estimating parameters of signals of this kind, the discrete polynomialphase transform (DPT), [3], later called highorder ambiguity function, [4], was proposed. The algorithm was extended to deal with multiple component signals in [2, 5, 6]. When estimating parameter...
On the Spectral Properties of PolynomialPhase Signals
, 1998
"... Polynomialphase signals (PPS's), i.e., signals parameterized as s(t)=A exp(j s(t)=A exp(j s(t)=A exp(j2 ), have been extensively studied and several algorithms have been proposed to estimate their parameters. From both the application and the theoretical points of view, it is particularly ..."
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Polynomialphase signals (PPS's), i.e., signals parameterized as s(t)=A exp(j s(t)=A exp(j s(t)=A exp(j2 ), have been extensively studied and several algorithms have been proposed to estimate their parameters. From both the application and the theoretical points of view, it is particularly important to know the spectrum of this class of signals. Unfortunately, the spectrum of PPS's of generic order is not known in closed form, except for first and secondorder PPS's. The aim of this letter is to provide an approximate behavior of the spectrum of PPS's of any order. More specifically, we prove that: i) the spectrum follows a power law behavior f , with fl =(M 0 2)=(M 0 1) fl =(M 0 2)=(M 0 1) fl =(M 0 2)=(M 0 1); ii) the spectrum is symmetric for MMM even and is strongly asymmetric for MMM odd; and iii) the maximum of the spectrum has an upper bound proportional to T and a lower bound proportional to . These results are useful to predict the performance of the socalled high order ambiguity function (HAF) and the ProductHAH (PHAF), specifically introduced to estimate the parameters of PPS's, when applied to multicomponent PPS's.
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
Estimating Parameters Of Polynomial Phase Signals By Tracking Algorithms
"... A recently proposed "multiple frequency tracker" in combination with a polynomial fitting procedure are shown to perform well in estimating parameters of polynomial phase signals. In comparison with the popular discrete polynomialphase transform, the proposed method is shown to have a significantly ..."
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A recently proposed "multiple frequency tracker" in combination with a polynomial fitting procedure are shown to perform well in estimating parameters of polynomial phase signals. In comparison with the popular discrete polynomialphase transform, the proposed method is shown to have a significantly lower SNR threshold, while retaining a low computational complexity. 1. INTRODUCTION Polynomial phase signals are encountered for example in pulse compression radar systems, where the signal components have polynomial phase if observed objects are in motion, [1]. Another application might be in modeling certain animal sounds, [1]. For these applications, signals with a quadratic or cubic polynomial phase, i.e. linear and quadratic frequency modulated (FM) signals, are the most important. For estimating parameters of linear FM signals there exists a large amount of literature, see e.g. [8] and the referencies therein. Hence the focus of this paper is on parameter estimation of quadratic FM...
Multicomponent Polynomial Phase Signal Analysis Using a Tracking Algorithm
, 1999
"... We describe an efficient technique analyzing signals that comprise a number of polynomial phase components. The technique is based on a recently proposed "multiple frequency tracker", an algorithm for recursive estimation of parameters of multiple sine waves in noise. It has a relatively low SNR thr ..."
Abstract
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We describe an efficient technique analyzing signals that comprise a number of polynomial phase components. The technique is based on a recently proposed "multiple frequency tracker", an algorithm for recursive estimation of parameters of multiple sine waves in noise. It has a relatively low SNR threshold and moderate computational complexity. 1 Introduction Polynomial phase signals are encountered for example in pulse compression radar systems, [1], in synthetic aperture radar imaging and mobile communications, [2], or in modeling certain animal sounds, [1]. For these applications, signals with a quadratic and cubic polynomial phase, i.e. linear and quadratic frequency modulated (FM) signals, are the most important. For estimating parameters of signals of this kind, the discrete polynomialphase transform (DPT), [3], later called highorder ambiguity function, [4], was proposed. The algorithm was extended to deal with multiple component signals in [2, 5, 6]. When estimating parameter...
Correspondence SubspaceBased Algorithm for Parameter Estimation of Polynomial Phase Signals
"... Abstract—In this correspondence, parameter estimation of a polynomial phase signal (PPS) in additive white Gaussian noise is addressed. Assuming that the order of the PPS is at least 3, the basic idea is first to separate its phase parameters into two sets by a novel signal transformation procedure, ..."
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Abstract—In this correspondence, parameter estimation of a polynomial phase signal (PPS) in additive white Gaussian noise is addressed. Assuming that the order of the PPS is at least 3, the basic idea is first to separate its phase parameters into two sets by a novel signal transformation procedure, and then the multiple signal classification (MUSIC) method is utilized for joint estimating the phase parameters with secondorder and above. In doing so, the parameter search dimension is reduced by a half as compared to the maximum likelihood and nonlinear least squares approaches. In particular, the problem of cubic phase signal estimation is studied in detail and its simplification for a chirp signal is given. The effectiveness of the proposed approach is also demonstrated by comparing with several conventional techniques via computer simulations. Index Terms—Parameter estimation, polynomial phase signal, subspace method. I.
Characterization of Signalbased Automated Information Processing in Distributed Systems for Environmental Surveillance Monitoring
"... Abstract—The work presents results of on going research on signalbased automated information processing in distributed systems. Some results are presented in the context of a grid services infrastructure for environmental surveillance monitoring applications. The research work uses concepts, princi ..."
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Abstract—The work presents results of on going research on signalbased automated information processing in distributed systems. Some results are presented in the context of a grid services infrastructure for environmental surveillance monitoring applications. The research work uses concepts, principles, rules, and techniques of informationbased complexity, nonabelian signal processing, graph algebras, and signalbased holomorphic information processing to characterized flow and computational complexities of informationtouser (I2U) processes in a distributed information processing environment, calling this approach informationtouser processing complexity. Information flow characterization in a distributed information processing (DIP) system is defined as the study of attributes associated with the structure, content, transferring, and meaning of information as it is carried by signalmessages coded from observable entities
Estimating Multiple FrequencyHopping Signal Parameters via Sparse Linear Regression
"... Abstract—Frequency hopping (FH) signals have welldocumented merits for commercial and military applications due to their nearfar resistance and robustness to jamming. Estimating FH signal parameters (e.g., hopping instants, carriers, and amplitudes) is an important and challenging task, but optimu ..."
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Abstract—Frequency hopping (FH) signals have welldocumented merits for commercial and military applications due to their nearfar resistance and robustness to jamming. Estimating FH signal parameters (e.g., hopping instants, carriers, and amplitudes) is an important and challenging task, but optimum estimation incurs an unrealistic computational burden. The spectrogram has long been the starting nonparametric estimator in this context, followed by line spectra refinements. The problem is that hop timing estimates derived from the spectrogram are coarse and unreliable, thus severely limiting performance. A novel approach is developed in this paper, based on sparse linear regression (SLR). Using a dense frequency grid, the problem is formulated as one of underdetermined linear regression with a dual sparsity penalty, and its exact solution is obtained using the alternating direction method of multipliers (ADMoM). The SLRbased approach is further broadened to encompass polynomialphase hopping (PPH) signals, encountered in chirp spread spectrum modulation. Simulations demonstrate that the developed estimator outperforms spectrogrambased alternatives, especially with regard to hop timing estimation, which is the crux of the problem. Index Terms—Compressive sampling, frequency hopping signals, sparse linear regression, spectrogram, spread spectrum signals. I.
An Optimisation Approach to Robust Estimation of Multicomponent Polynomial Phase Signals in NonGaussian Noise
"... Abstract—Inthispaper 1 we address the problem of estimating the parameters of multicomponent polynomial phase signals in impulsive noise which arises in many practical situations. In the presence of this nonstandard noise, existing techniques perform can poorly. We propose a nonlinear Mestimation ..."
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Abstract—Inthispaper 1 we address the problem of estimating the parameters of multicomponent polynomial phase signals in impulsive noise which arises in many practical situations. In the presence of this nonstandard noise, existing techniques perform can poorly. We propose a nonlinear Mestimation approach to improve the existing techniques. The phase parameters are obtained by solving a nonlinear optimisation problem. A procedure is proposed to find the global minimum at low computational cost. Simulation examples show the proposed method performs better than existing methods. I.
doi:10.1155/2009/727034 Research Article Adaptive Algorithm for ChirpRate Estimation
, 2009
"... Chirprate, as a second derivative of signal phase, is an important feature of nonstationary signals in numerous applications such as radar, sonar, and communications. In this paper, an adaptive algorithm for the chirprate estimation is proposed. It is based on the confidence intervals rule and the ..."
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Chirprate, as a second derivative of signal phase, is an important feature of nonstationary signals in numerous applications such as radar, sonar, and communications. In this paper, an adaptive algorithm for the chirprate estimation is proposed. It is based on the confidence intervals rule and the cubicphase function. The window width is adaptively selected to achieve good tradeoff between bias and variance of the chirprate estimate. The proposed algorithm is verified by simulations and the results show that it outperforms the standard algorithm with fixed window width. Copyright © 2009 Igor Djurović et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.