Chair: Jitendra K. Tugnait, Auburn University (USA)
Robert D. Nowak, University of Wisconsin-Madison (USA)
Barry D. Van Veen, University of Wisconsin-Madison (USA)
To reduce the number of parameters in the Volterra filter a tensor product basis approximation is considered. The approximation can be implemented much more efficiently than the original Volterra filter. In addition, because the design methods are based on partial characterization of the Volterra filter, the approximations are also useful in reducing the complexity of identification and modelling problems. Useful bounds are obtained on the approximation error.
Birsen Yaz c, G.E. Corporate Research and Development
Rangasami L. Kashyap, Purdue University (USA)
In this paper, we introduce a class of stochastic processes whose correlation function obeys a structure of the form, E[X(t)X(). We refer to these processes as second order self-similar processes. This class of processes include fractional Brownian motion, a special case. We define a concept of autocorrelation and develop a spectral analysis framework via generalized Mellin transform for the proposed class. Additionally, we establish a relationship between the proposed self-similar processes and generalized linear scale invariant system theory. We give specific models and demonstrate their ability to model 1/f phenomena.
Branko Ristic, Queensland University of Technology (AUSTRALIA)
Geoff Roberts, Queensland University of Technology (AUSTRALIA)
Boualem Boashash, Queensland University of Technology (AUSTRALIA)
This paper develops a novel concept of higher-order moment and cumulant functions in the compress/stretch domain, and their corresponding higher-order spectra in the scale domain. Then higher-order Q time-scale distributions are introduced and their properties are investigated. The importance of the paper is to link the recently developed concept of scale signal representations with well established and important methods of higher-order spectral analysis.
P. Duvaut, ETIS-ENSEA
T. Gouraud, Universite de Nantes (FRANCE)
This paper introduces a new time-frequency representation called the bicorspectral transform BET, derives most of its theoretical properties, and details relevant applications. This representation is devoted to non-gaussian processes either stationary or not that exhibit non-vanishing third order moments. It is also closely related to the deterministic correlation between the signal and its Wigner-Ville distribution which yields efficient implementation with almost the same numerical complexity as a Pseudo-Wigner-Ville representation.
J.M. Le Caillec, Telecom Bretagne
R. Garello, Telecom Bretagne
B. Chapron, IFREMER (FRANCE)
Higher order moments have been, for the last decade, an important field of interest, but generally limited to one dimensional signal cases. We introduce in this paper 2D bispectrum to detect nonlinearity in the SAR image mapping process, by using th bicoherence of 2D signal which is theoretically flat over all frequencies, if the process is linear. Two bicoherency estimators are developed, the first one using direct method for bispectral estimation and the periodogram for spectral estimator, and the second one based on indirect method and correlogram. In order to validate our nonlinearity detection method, we have tested it on to simulated images, a linear one and a non-linear one, and then on two SAR images, one seeming to be non-linear. Conclusions are drawn by comparing SAR image and simulated image bicoherencies.
Paul D. Burns, Auburn University (USA)
Zhi Ding, Auburn University (USA)
The problem of exploiting cyclostationary statistical information for the purpose of array processing is addressed. Techniques for exploiting second order periodic information are proposed for the enhancement of cyclic-MUSIC and Self COherent REstoration (SCORE) algorithms. The robustification of both cyclic MUSIC and SCORE can be accomplished by increasing the amount of cyclic information used. Simulation results are presented which show the performance improvement by the modified algorithms.
Guotong Zhou, University of Virginia
Ananthram Swami, Malgudi Systems (USA)
We consider the parameter estimation problem for a class of amplitude modulated polynomial phase signals (PPS), observed in noise. The main contributions of this paper are: (1) We prove that the High-order Ambiguity Function (HAF) is invariant to certain types of amplitude modulation; thus, phase parameter estimation proceeds as in the constant amplitude case. (2) We derive the Cramer-Rao bounds for both the amplitude and phase parameters, when the additive noise is white Gaussian. (3) We show that the HAF is almost additive for multi-component PPS. (4) We establish the covariance bounds for the nonlinear least squares estimator when the additive noise is colored (non)Gaussian, and satisfies some weak mixing conditions.
Stephen M. Kogon, Georgia Institute of Technology
Dimitris G. Manolakis, Boston College (USA)
In this paper, two models of long-range dependence with finite and infinite variance that have recently been proposed in the mathematics literature are considered. The models are used for the characterization of experimental data in order to determine the possible benefits they offer over existing models. They are presented under a unified framework and their similarities and differences are investigated by applying the models to real world data in the form of infrared background signals.
Shankar Prakriya, University of Toronto (CANADA)
Dimitrios Hatzinakos, University of Toronto (CANADA)
A simple method is proposed for blind identification of discrete-time nonlinear models consisting of two Linear Time Invariant (LTI) subsystems separated by a polynomial-type Zero Memory Nonlinearity (ZMNL) of order N (the LTI-ZMNL-LTI model). When the input to the model is a circularly symmetric Gaussian sequence, the linear subsystems of the model can be identified efficiently using slices of the N+1^th order polyspectrum of the output signal, even when the second linear subsystem is of Non-Minimum Phase (NMP). The ZMNL coefficients need not be known. The order N of the nonlinearity can, in principle, be estimated from the received signal. The methods possess noise suppression characteristics. Computer simulations support the theory.