Results 1  10
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14
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 particul ..."
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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.
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 l ..."
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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...
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
EURASIP Journal on Applied Signal Processing 2005:17, 2856–2873 c ○ 2005 Hindawi Publishing Corporation TimeFrequency Analysis Using WarpedBased HighOrder Phase Modeling
"... The highorder ambiguity function (HAF) was introduced for the estimation of polynomialphase signals (PPS) embedded in noise. Since the HAF is a nonlinear operator, it suffers from noisemasking effects and from the appearance of undesired crossterms when multicomponents PPS are analyzed. In order ..."
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The highorder ambiguity function (HAF) was introduced for the estimation of polynomialphase signals (PPS) embedded in noise. Since the HAF is a nonlinear operator, it suffers from noisemasking effects and from the appearance of undesired crossterms when multicomponents PPS are analyzed. In order to improve the performances of the HAF, the multilag HAF concept was proposed. Based on this approach, several advanced methods (e.g., product highorder ambiguity function (PHAF)) have been recently proposed. Nevertheless, performances of these new methods are affected by the error propagation effect which drastically limits the order of the polynomial approximation. This phenomenon acts especially when a highorder polynomial modeling is needed: representation of the digital modulation signals or the acoustic transient signals. This effect is caused by the technique used for polynomial order reduction, common for existing approaches: signal multiplication with the complex conjugated exponentials formed with the estimated coefficients. In this paper, we introduce an alternative method to reduce the polynomial order, based on the successive unitary signal transformation, according to each polynomial order. We will prove that this method reduces considerably the effect of error propagation. Namely, with this order reduction method, the estimation error at a given order will depend only on the performances of the estimation method.
EURASIP Journal on Applied Signal Processing 2005:17, 2804–2815 c ○ 2005 Hindawi Publishing Corporation TeagerKaiser Energy and HigherOrder Operators in WhiteLight Interference Microscopy for Surface Shape Measurement
"... In whitelight interference microscopy, measurement of surface shape generally requires peak extraction of the fringe function envelope. In this paper the TeagerKaiser energy and higherorder energy operators are proposed for efficientextractionofthe fringe envelope. These energy operators are comp ..."
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In whitelight interference microscopy, measurement of surface shape generally requires peak extraction of the fringe function envelope. In this paper the TeagerKaiser energy and higherorder energy operators are proposed for efficientextractionofthe fringe envelope. These energy operators are compared in terms of precision, robustness to noise, and subsampling. Flexible energy operators, depending on order and lag parameters, can be obtained. Results show that smoothing and interpolation of envelope approximation using spline model performs better than Gaussianbased approach.
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.
Author manuscript, published in "IEEE International Symposium on Industrial Electronics, Montreal: Canada (2006)" DOI: 10.1109/ISIE.2006.295519 TimeFrequency Characterization using Instantaneous Moment Concept:
, 2008
"... Abstract The instantaneous frequency law (IFL) is a very important element when the physical parameters of the corresponding signal have to be evaluated. Blind equalisation, modulation recognition and mechanical diagnostic are just three domains where the nonstationarity behavior of the signal imp ..."
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Abstract The instantaneous frequency law (IFL) is a very important element when the physical parameters of the corresponding signal have to be evaluated. Blind equalisation, modulation recognition and mechanical diagnostic are just three domains where the nonstationarity behavior of the signal imposes the IFL estimation. Generally, an IFL is composed by slowly varying timefrequency structures separated by fast transitions which could be considered as phase discontinuities. Digital phase modulations or signals propagated trough a multipath channel are typical examples of IFLs having fast transient parts. The common methods employed for these operations are wavelet transform and Cohen’s class timefrequency representation, respectively. In this paper we propose an alternative based on the instantaneous moments. By an appropriate choice of the moment order and lags it is possible to accurately estimate the both transient and slowly timefrequency parts. While this method uses one dimensional data and, thanks to its recursive structure, it is well suited for real time applications. Therefore, its realtime implementation on TMS320C6x structure is described. On the other hand, few examples on realistic data will show the practical interest for this method. I.
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 l ..."
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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...