H.O.S.'97 Plenary Sessions

Monday, July 21, 1997, 8:00 - 8:50 AM

High-order Cyclostationary Signal Analysis: An overview
Dr. Georgios Giannakis, Univ. of Virginia (USA)


Processes encountered in statistical signal processing, communications, and time series analysis applications, are often assumed stationary. Due to the varying nature of physical phenomena and certain manmade operations however, time-invariance and the related notion of stationarity are often violated in practice. In this talk, I will focus on cyclostationary processes which are characterized by the periodicity they exhibit in their second- and/or higher-order statistical descriptors. Periodicity is omnipresent in real life problems entailing phenomena and operations of repetitive nature: communications, geophysical and atmospheric sciences (hydrology, oceanography, meteorology, climatology), rotating machinery, econometrics, and biological systems. Background material will deal with polyspectral representations, sample estimation of cyclic statistics, testing a time series for second- and high-order cyclostationarity, and noise suppression by joint exploitation of cyclostationarity and non-Gaussianity. The diversity offered by periodic variations will be emphasized in the context of blind identification of time-invariant and periodically varying systems and separation of cyclostationary signals on the basis of their cycles. Specific applications will include time delay estimation, harmonic retrieval in the presence of multiplicative noise, modeling with systematically missing observations, polynomial phase signals for modeling motion induced variations, equalization of random channels, and generalized differential encoding of communication
Tuesday, July 22, 1997, 8:00 - 8:50 AM

Signal Processing with Alpha-Stable Distributions: Current and Future Trends
Dr. Chrysostomos L. Nikias, Univ. of Southern California (USA)


The importance of extending the statistical signal processing methodology to the alpha-stable framework is apparent. First, scientists and engineers have started to appreciate lower-order moments and the elegant scaling and self-similarity properties of stable distributions. Additionally, real life applications exist in which impulsive channels tend to produce large-amplitude, short-duration interferences more frequently than Gaussian channels do. The stable law has been shown to successfully model noise over certain impulsive channels. In this talk, we present an overview of alpha-stable processes and lower-order statistics. In addition, we review recent advanced techniques for detection, parameter estimation, and system identification in the presence of signals/noise modeled as stable processes. Finally, we address future trends on signal processing within the alpha-stable framework.
Wednesday, July 23, 1997, 8:00 - 8:50 AM

Cumulant Tensors
Dr. Pierre Comon, EURECOM (FRANCE)


Cumulants of multidimensional random variables satisfy the properties that allow them to be considered as tensors. Most cumulant-based signal processing algorithms actually use slices of those tensors, mainly because numerical algorithms available today are only able to manipulate matrices. In addition, very few works in the literature have addressed the problem of decomposing or factorizing tensors. This would be a discrepancy if the problem was not so difficult, as emphasized in the talk. However, it is still possible to establish some links with the Eigenvalue decomposition, the congruent diagonalization, or the Cholesky factorization of matrices. But striking differences can be pointed out. It is hoped that these first basic statements will motivate further developments of tensor-based algorithms.