Georges Delaunay

Secure digital communication using chaotic modulation with feedback

In this note we propose a new chaotic modulation schema with output feedback. It is shown that the receiver can synchronize with the transmitter with any desired rate. Moreover, this approach can be applied to a large class of chaotic systems and provides higher security against an intruder. The robustness of our scheme with respect to noise is illustrated and compared, to the symmetric chaos shift keying method.

Multitime frequency classifiers for neighboring modulations in a multiplicative noise environment

This communication presents two new classification algorithms based on time varying higher order statistics (TVHOS). These two algorithms benefit from the advantageous localization properties provided by TVHOS4 for instantaneous frequency laws disrupted by multiplicative noise. The classification scheme used is a bank of several normalized TVHOS4 correlators. Simulations illustrate successful performance of the classification algorithms for different situations and especially if the SNR is higher than -7 dB.

Time varying higher order statistics for FM signals analysis and decision

Abstract Time varying higher order spectra (TVHOS) are designed for non-Gaussian non-stationary signal processing. However, these complex representations must be well understood to allow some interesting improvements despite their complexity growth. This paper presents the common TVHOS representations and provides an analysis of the “cross-terms” linked to their non-linear structure. Some of these representations are used for FM signal analysis and decision in a context of multiplicative and additive noise. Two new decision schemes using 4th order moment and cumulant representations are presented and their performances, compared with the equivalent 2nd approach (based on Wigner spectrum), are discussed.

A new criterion for second order cyclostationary blind source separation

In this paper, we propose a new blind separation criterion for second order cyclostationary sources with known and different cyclic frequencies. The method results from the spectral analysis; it is based on the use of the second order cyclostationary characteristics of the source signals. The theoretical results are presented and proved. The computer simulations show a good performance of the proposed method in comparison with Sobi, CycloSobi and Jade algorithms.

Some new results on the discrete bispectrum

This paper presents some new results concerning the bispectrum of sampled signals. We show that sampling a stationary signal at Fs=2B usually implies a non-zero outer triangle (OT) domain in the bispectrum due to overlapping. Moreover, we pointed out that processes (stationary or not) sampled at Fs>3B are always zero in the OT (no overlapping). Finally, we propose an empirical method for which a non-zero OT indicates that the signal is really non-stationary and we propose to combine this approach with the Hinich stationarity test (Hinich 1990, and Hinich and Messer 1995).