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ABSTRACT: In this paper we propose a new method for estimating the ambiguity function (AF) of a random process with limited spreading support. The observed process is modelled as the aggregation of a non-stationary signal of interest and noise. As the AF has limited spreading, thresholding is a suitable estimation procedure. Some key stochastic properties of the empirical ambiguity function are derived to obtain a suitable threshold. Based on a median absolute deviation estimator for the variance, we derive a suitable threshold, which forms the basis for our proposed estimator. The estimator is tested on both artificial and real signals, and our results demonstrate a remarkably high resolution and reduced variance.
Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on; 05/2008 · 4.63 Impact Factor
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ABSTRACT: The relative height of the seafloor can be estimated by using two vertically displaced receivers. In this paper, we propose techniques to improve the accuracy of the estimated height. Our results are based on the use of synthetic aperture sonar (SAS) imaging, which implies coherent addition of complex images acquired from a moving platform. The SAS processing improves the along-track (or azimuth) resolution, as well as the signal-to-noise ratio (SNR), which in turn improves the estimated height accuracy. We show that the shift of the effective center frequency induced by coherent, frequency-dependent scattering affect the time-delay estimates from complex cross correlations, and we propose a correction technique for broadband signals with uneven magnitude spectra. To reduce the effect of geometrical decorrelation and increase the coherence between the images, we beamform the sonar images onto an a priori estimate of the seafloor height before correlating. We develop a mathematical model for the imaging geometry. Finally, we demonstrate our proposed estimators by providing relative seafloor height estimates from real aperture and SAS images, obtained during the InSAS-2000 experiment at Elba Island in Italy. In particular, we demonstrate that the SAS image quality is significantly improved by inclusion of the height estimates as a priori information.
IEEE Journal of Oceanic Engineering 11/2007; · 0.95 Impact Factor
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ABSTRACT: Complex-valued nonstationary random processes have nonvanishing complementary second-order moment functions. In this paper, we propose generalized dual-frequency and time-frequency coherence functions for harmonizable processes. The proposed generalized spectral coherences are based on widely linear estimators, and they result in coherence measures that combine Hermitian and complementary moment functions. We show that for analytic processes, and more surprisingly also for real-valued processes, additional second-order information becomes available through the generalized coherences. We offer illuminating geometrical interpretations of the proposed coherences through Hilbert space inner product formulations. Finally, we extend the theory to generalized cross-coherences between pairs of harmonizable processes
IEEE Transactions on Signal Processing 07/2007; · 2.63 Impact Factor
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ABSTRACT: A complex random vector is called improper if it is correlated with its complex conjugate. We present a hypothesis test for impropriety based on a generalized likelihood ratio (GLR). This GLR is invariant to linear transformations on the data, including rotation and scaling, because propriety is preserved by linear transformations. More specifically, we show that the GLR is a function of the squared canonical correlations between the data and their complex conjugate. These canonical correlations make up a complete, or maximal, set of invariants for the Hermitian and complementary covariance matrices under linear, but not widely linear, transformation
IEEE Signal Processing Letters 08/2006; · 1.39 Impact Factor
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ABSTRACT: A complex random vector is called improper if it is correlated with its complex conjugate. In this paper, we present a generalized likelihood ratio test (GLRT) for impropriety. This test is compelling because it displays the right invariances: The proposed GLR is invariant to linear transformations on the data, including rotation and scaling, just as propriety is preserved by linear transformations. Because canonical correlations make up a complete, or maximal, set of invariants for the Hermitian and complementary covariance matrices under linear transformations, the GLR can be shown to be a function of the squared canonical correlations between the data and its complex conjugate. This validates our intuition that the internal coordinate system should not matter for this hypothesis test
Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings. 2006 IEEE International Conference on; 06/2006 · 4.63 Impact Factor
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ABSTRACT: In this brief, we introduce a subspace theory for differential chaos-shift keying (DCSK) systems. We show that DCSK systems operate by transmission of chaotic signals residing in a low-dimensional subspace. The subspace formalism of DCSK schemes leads to the derivation of useful subspace detectors that can be applied to decode the DCSK signal for various types of channels. Closed form expressions for the bit error rate is derived for an M-ary FM-version of DCSK, under the assumption of orthogonal subspace generating vectors. Numerical simulations demonstrate that the proposed subspace detector in general outperforms the conventional correlation detector for DCSK
Circuits and Systems II: Express Briefs, IEEE Transactions on 02/2006; · 1.41 Impact Factor
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ABSTRACT: We have analyzed the sound of an electric guitar that has been amplified by a high-quality all-tube amplifier, and emitted by means of a speaker cabinet. We re-amplified a recording of a clean guitar through a state-of-the-art all-tube amplifier at three different preamplifier gain settings: one clean, one half-distorted, and one massively distorted. Spectral analysis of recordings of the three signals exhibited a remarkably rich overtone spectrum, and we observed that only the high frequency part of the spectrum was boosted by an increase in the distortion levels. A bispectral analysis of the amplified guitar sound showed that quadratic nonlinearities are responsible for coherent phase coupling among the partials, and that the fraction of the total power which is due to quadratic nonlinearities is larger for the clean sound than for the distorted sound. Finally, a dual-frequency analysis showed that the sound, even for the sustained part of a single string pluck, is in fact a nonstationary random process. Our analysis showed that the guitar tone should be classified as an (almost) cyclostationary random process.
Applications of Signal Processing to Audio and Acoustics, 2005. IEEE Workshop on; 11/2005
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ABSTRACT: Based on the Cramer-Loeve spectral representation for a harmonizable random process, the Rihaczek distribution is a time- and frequency-shift covariant, bilinear time-frequency distribution. It can be expressed as a complex Hilbert space inner product between the time series and its infinitesimal stochastic Fourier generator. We show that we may attach an illuminating geometry to this inner product, wherein the cosine-squared of the angle between the time series and its infinitesimal stochastic Fourier generator is given by the Rihaczek distribution. We propose to construct estimators of the Rihaczek distribution using a factored kernel in Cohen's class of bilinear time-frequency distributions
Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on; 10/2005
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ABSTRACT: Fractional Brownian motion (fBm) is a useful non-stationary model for certain fractal and long-range dependent processes of interest in telecommunications, physics, biology, and finance. Conventionally, the power spectrum of fBm is claimed to be a fractional power-law. However, fBm is not a wide-sense stationary process, so the precise meaning of this spectrum is unclear. In this paper, we model and analyze fBm in the context of harmonizable random processes. We derive and interpret exact expressions for novel useful complex valued second-order moment functions for fBm. These moment functions are time-frequency and dual-frequency correlation functions, connecting the random process to its infinitesimal random Fourier generator. In particular, we derive and discuss the time-frequency Rihaczek spectrum, and the dual-frequency Loeve spectrum. Our main finding is that the dual-frequency spectrum of fBm has its spectral support confined to three discrete lines. This leads to the surprising conclusion that for fBm, the DC component of the infinitesimal Fourier generator is correlated with ail other frequencies of the Fourier generator. We propose and apply multitaper based estimators for the moment functions, and numerical estimates based on synthetic fBm data and real world earthquake data confirm our theoretical results
Statistical Signal Processing, 2005 IEEE/SP 13th Workshop on; 08/2005
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ABSTRACT: The Rihaczek distribution for stochastic signals is a time- and frequency-shift covariant bilinear time-frequency distribution (TFD) based on the Crame´r-Loe`ve spectral representation for a harmonizable process. It is a complex Hilbert space inner product (or cross correlation) between the time series and its infinitesimal stochastic Fourier generator. To this inner product, we may attach an illuminating geometry, wherein the cosine squared of the angle between the time series and its infinitesimal stochastic Fourier generator is given by the Rihaczek distribution. The Rihaczek distribution also determines a time-varying Wiener filter for estimating a time series from its infinitesimal stochastic Fourier generator and measures the resulting error covariance. We propose a factored kernel to construct estimators of the Rihaczek distribution that are contained in Cohen's class of bilinear TFDs.
IEEE Signal Processing Letters 05/2005; · 1.39 Impact Factor
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ABSTRACT: In this paper we consider shape classification of partially occluded objects. We model the occlusion as non-Gaussian noise, and apply robust subspace detectors in the classification module. We show that the robust subspace detectors can be formulated as a weighted subspace detector, and the elements in the boundary vector will be weighted before they are matched. The part of the boundary vector that corresponds to the occluded part of the object, will be suppressed by the weight vector, and hence have a reduced effect on the classification performance. The detectors are demonstrated on fish species classification applications.
Image Processing, 2004. ICIP '04. 2004 International Conference on; 11/2004
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ABSTRACT: We present a definition of a dual-frequency dual-wavenumber cross-spectrum of two nonstationary and inhomogeneous harmonizable random fields, which is in fact a generalization of the Loeve (dual-frequency) cross-spectrum of two random processes. Furthermore, a geometric argument shows that a proper normalization yields a natural measure of cross-coherence, and application of the Cauchy-Schwarz inequality results in a necessary and sufficient condition for full cross-coherence. Finally, estimators of the cross-spectrum and the cross-coherence based on the multitaper approach are suggested, and tested on synthetic array processing data.
Sensor Array and Multichannel Signal Processing Workshop Proceedings, 2004; 08/2004
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ABSTRACT: Harmonizable processes constitute an important class of non-stationary stochastic processes. In this paper we study the important extension to multivariate harmonizable random fields. We derive the multivariate-multidimensional Rihaczek spectrum and show that it determines a complex time-frequency varying Wiener filter for approximating a multivariate random field from its infinitesimal Fourier generator. We derive the time-frequency coherence function, and generalize it to canonical correlations between a time domain subspace and a frequency domain subspace. We show how to construct estimators, and we finally demonstrate the theoretical concepts by the analysis of synthetic data.
Sensor Array and Multichannel Signal Processing Workshop Proceedings, 2004; 08/2004
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ABSTRACT: In this paper, we propose and design robust subspace detectors for classification of multidimensional subspace signals. Using the principle of M-estimators and least-median-of-squares (LMedS), we formulate the robust subspace detectors as weighted subspace detectors, where we weigh the rows of the measurement matrix prior to the signal matching. The detectors are demonstrated numerically by communication signals transmitted over an unknown frequency selective channel in impulsive noise, and shape classification of partially occluded two-dimensional objects. In both cases, the proposed robust subspace detectors outperform the classical subspace detector.
Sensor Array and Multichannel Signal Processing Workshop Proceedings, 2004; 08/2004
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ABSTRACT: We present a definition of a dual-frequency dual-wavenumber cross-spectrum of two nonstationary and inhomogeneous harmonizable random fields, which is in fact a generalization of the Loeve (dual-frequency) cross-spectrum of two random processes. Furthermore, a geometric argument shows that a proper normalization yields a natural measure of cross-coherence, and application of Cauchy-Schwarz's inequality results in a necessary and sufficient condition for full cross-coherence. Finally, estimators of the cross-spectrum and the cross-coherence based on the multitaper approach are suggested, and tested on simulated data.
Acoustics, Speech, and Signal Processing, 2004. Proceedings. (ICASSP '04). IEEE International Conference on; 06/2004 · 4.63 Impact Factor
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ABSTRACT: We present a definition of a dual-frequency dual-wave-number cross-spectrum of two nonstationary and inhomogeneous harmonizable random fields, which is in fact a generalization of the Loeve (dual-frequency) cross-spectrum of two random processes. Furthermore, a geometric argument shows that a proper normalization yields a natural measure of cross-coherence, and application of Cauchy-Schwarz' inequality results in a necessary and sufficient condition for full cross-coherence. Finally, estimators of the cross-spectrum and the cross-coherence based on the multitaper approach are suggested, and tested on simulated data.
Signals, Systems and Computers, 2003. Conference Record of the Thirty-Seventh Asilomar Conference on; 12/2003
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ABSTRACT: We have examined certain statistical aspects of seabed images formed by wideband synthetic aperture sonar. In particular, we have formed high-quality data-adaptive non-parametric kernel estimates from the envelope images. In most cases, the estimated tails of the distribution appear to be substantially heavier than those of the Rayleigh-distribution. Parametric approaches, e.g., fits of the data to a Rayleigh mixture, suggest that the data may be described by a mixture of 2 to 3 Rayleigh populations. Images formed by various degrees of preprocessing are analyzed in this manner. In particular, we examine the dependence on the physical resolution, and on using frequency sub-bands for the image formation.
OCEANS 2003. Proceedings; 10/2003
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ABSTRACT: Harmonizable processes constitute an important class of nonstationary stochastic processes. We present a theory of polyspectra (higher order moment spectra) for the harmonizable class. We define and discuss four basic quantities: the nth-order moment function, the nth-order time-frequency polyspectrum, the nth-order ambiguity function, and the nth-order frequency-frequency polyspectrum. The latter generalizes the conventional polyspectrum to nonstationary stochastic processes. These four functions are related to one another by Fourier transforms. We show that the frequency and time marginals of the time-frequency polyspectrum are the instantaneous nth-order moment and the conventional nth-order stationary polyspectrum, respectively. All quantities except the nth-order ambiguity function allow for insightful interpretations in terms of Hilbert space inner products. The inner product picture leads to two novel and very powerful definitions of polycoherence for a nonstationary stochastic process. The polycoherences are objective measures of stationarity to order n, which can be used to construct various statistical tests. Finally, we give some specific examples and apply the theory to linear time-varying systems, which are popular models for fading multipath communication channels.
IEEE Transactions on Signal Processing 06/2003; · 2.63 Impact Factor
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ABSTRACT: Harmonizable processes form an important class of nonstationary stochastic processes. In this paper we present a theory of higher-order moment spectra (polyspectra) for the harmonizable class. We show that there are four basic quantities, the n-th order moment function, the n-th order time-varying polyspectrum, the n-th order ambiguity function, and the n-th order spectral correlation function that need to be considered. We offer interpretations of the polyspectra in terms of Hilbert space inner products. Based on the inner product interpretations, we derive two novel definitions of n-th order polycoherence. The polycoherences are objective measures of stationarity to order n, which can be used to construct various statistical tests.
Signals, Systems and Computers, 2002. Conference Record of the Thirty-Sixth Asilomar Conference on; 12/2002
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ABSTRACT: The normal inverse Gaussian (NIG) distribution is a variance-mean mixture of a Gaussian with an inverse Gaussian distribution. The NIG can serve as a model for data that are heavy-tailed (lep-tokurtic), and the model was first introduced in empirical finance by Bamdorrf-Nielsen in 1995. We present the important extension to multivariate NIG (MNIG) distributions, and we discuss some of the basic properties of the MNIG. We furthermore discuss several new and important properties of the MNIG. An important part of the paper deals with the derivation of a fast and accurate method for generating i.i.d. MNIG-distributed variates. We also present a multivariate expectation-maximization (EM) algorithm for the estimation of the scalar, vector, and matrix parameters of the MNIG. Finally, we present a fit of the bivariate NIG to an actual multichannel radar data set, where we have applied our EM parameter estimation algorithm. From the insight we have gained, we conclude that the MNIG has numerous potential applications in multivariate data analysis and modeling, and that the simulation and estimation methods described may serve as important and useful tools in that respect
Acoustics, Speech, and Signal Processing, 2002. Proceedings. (ICASSP '02). IEEE International Conference on; 02/2002
