Jean-Christophe Cexus

EMD-Based Signal Filtering

In this paper, a signal-filtering method based on empirical mode decomposition is proposed. The filtering method is a fully data-driven approach. A noisy signal is adaptively decomposed into intrinsic oscillatory components called intrinsic mode functions (IMFs) by means of an algorithm referred to as a sifting process. The basic principle of the method is to make use of partial reconstructions of the signal, with the relevant IMFs corresponding to the most important structures of the signal (low-frequency components). A criterion is proposed to determine the IMF, after which, the energy distribution of the important structures of the signal overcomes that of the noise and that of the high-frequency components of the signal. The method is illustrated on simulated and real data, and the results are compared to well-known filtering methods. The study is limited to signals that were corrupted by additive white Gaussian noise and is conducted on the basis of extended numerical experiments.

IF estimation using empirical mode decomposition and nonlinear Teager energy operator

In this paper, a method based on the empirical mode decomposition (EMD) algorithm and Teager energy operator (TEO) is proposed to estimate the instantaneous frequency (IF) of a signal embedded in noise. IF is used to describe a signals frequency that varies with time. Both EMD and TEO deal with non-stationary signals. The signal is first band pass filtered into subsignals (components) called intrinsic mode functions (IMFs) with well defined IF. Each IMF is a zero-mean AM-FM component. Then TEO tracks the modulation energy of each IMF and estimates the corresponding IF. In order to show the effectiveness of the proposed method, results of IF estimation of noisy AM-FM signals are proposed.

Analysis of multicomponent LFM signals by Teager Huang-Hough transform

A novel detection approach of linear FM (LFM) signals, with single or multiple components, in the time-frequency plane of Teager-Huang (TH) transform is presented. The detection scheme that combines TH transform and Hough transform is referred to as Teager-Huang-Hough (THH) transform. The input signal is mapped into the time-frequency plane by using TH transform followed by the application of Hough transform to recognize time-frequency components. LFM components are detected and their parameters are estimated from peaks and their locations in the Hough space. Advantages of THH transform over Hough transform of Wigner-Ville distribution (WVD) are: 1) cross-terms free detection and estimation, and 2) good time and frequency resolutions. No assumptions are made about the number of components of the LFM signals and their models. THH transform is illustrated on multicomponent LFM signals in free and noisy environments and the results compared with WVD-Hough and pseudo-WVD-Hough transforms.

Cross ΨB-energy operator-based signal detectiona)

In this paper, two methods for signal detection and time-delay estimation based on the cross Psi(B)-energy operator are proposed. These methods are well suited for mono-component AM-FM signals. The Psi(B) energy operator measures how much one signal is present in another one. The peak of the Psi(B) operator corresponds to the maximum of interaction between the two signals. Compared to the cross-correlation function, the Psi(B) operator includes temporal information and relative changes of the signal which are reflected in its first and second derivatives. The discrete version of the continuous-time form of the Psi(B) operator, which is used in its implementation, is presented. The methods are illustrated on synthetic and real signals and the results compared to those of the matched filter and the cross correlation. The real signals correspond to impulse responses of buried objects obtained by active sonar in iso-speed single path environments.

An energy-based similarity measure for time series

A new similarity measure, called SimilB, for time series analysis, based on the cross--energy operator (2004), is introduced. is a nonlinear measure which quantifies the interaction between two time series. Compared to Euclidean distance (ED) or the Pearson correlation coefficient (CC), SimilB includes the temporal information and relative changes of the time series using the first and second derivatives of the time series. SimilB is well suited for both nonstationary and stationary time series and particularly those presenting discontinuities. Some new properties of are presented. Particularly, we show that as similarity measure is robust to both scale and time shift. SimilB is illustrated with synthetic time series and an artificial dataset and compared to the CC and the ED measures.

Generalized higher-order nonlinear energy operators

We extend and generalize the Teager-Kaiser [in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (1993), Vol. 3, p. 149] and the higher-order differential energy operators [IEEE Signal Process. Lett.2, 152 (1995)] to a large class of operators called higher-order energy operators. We show that for AM-FM signal demodulation, the introduced partial derivative orders have to satisfy certain conditions. These operators are parameterized for local processing of AM-FM signals. The operators are illustrated using synthetic signals and a real signal from light scanning interferometry.

Noise filtering using Empirical Mode Decomposition

In this paper a noise filtering method using the empirical mode decomposition (EMD) is proposed. The noisy signal is decomposed into oscillatory components called intrinsic mode functions (IMFs) using a process referred to as sifting. The basic idea of the proposed scheme is the partial re-construction of the signal using the IMFs corresponding to the most important structures of the signal (low frequency modes). A new criterion is proposed to determine the IMF after which the energy distribution of the important structures of the signal overcomes that of the noise and that of the high frequency components of the signal. The method is tested on simulated and real signals.

Two-dimensional continuous higher-order energy operators

An extension of the 2-D discrete Teager-Kaiser energy operator and the 1-D higher-order energy operators to the 2-D continuous case is proposed. These 2-D continuous operators are flexible enough to apply a large class of image gradient filters, and consequently different discrete energy operators are derived. Particularly, the proposed model takes into account the diagonal directions, through the partial derivatives. The obtained operators are computationally very simple, like the classical 2D Teager-Kaiser operator, and are well suited for image-processing applications such as image demodulation or image contrast enhancement. Results of demodulation of synthetic and real images, to estimate envelope information, are presented to show the feasibility of the proposed operators.

Features modeling with an α-stable distribution: Application to pattern recognition based on continuous belief functions

The aim of this paper is to show the interest in fitting features with an @a-stable distribution to classify imperfect data. The supervised pattern recognition is thus based on the theory of continuous belief functions, which is a way to consider imprecision and uncertainty of data. The distributions of features are supposed to be unimodal and estimated by a single Gaussian and @a-stable model. Experimental results are first obtained from synthetic data by combining two features of one dimension and by considering a vector of two features. Mass functions are calculated from plausibility functions by using the generalized Bayes theorem. The same study is applied to the automatic classification of three types of sea floor (rock, silt and sand) with features acquired by a mono-beam echo-sounder. We evaluate the quality of the @a-stable model and the Gaussian model by analyzing qualitative results, using a Kolmogorov-Smirnov test (K-S test), and quantitative results with classification rates. The performances of the belief classifier are compared with a Bayesian approach.

A combined Teager-Huang and Hough Transforms for LFM signals detection

A new method for linear FM (LFM) signals detection in the time-frequency plane using Teager-Huang Transform (THT) is proposed. Time-Frequency Representation (TFR) is viewed as an image where image processing techniques are applied to detect frequency patterns of interest. THT is used in conjunction with Hough Transform (HgT) called (THHT), where the output is a TFR free of cross-terms. THHT is applied to signals composed of LFM and the results are compared to Wigner-Ville Distribution-HgT and smoothed Wigner-Ville Distribution-HgT. Results show the good performance of the THHT in terms of detection and estimation compared to WVD based methods.