Georges Oppenheim

Wavelets and their applications

Notations. Introduction. Chapter 1. A Guided Tour. Chapter 2. Mathematical Framework. Chapter 3. From Wavelet Bases to the Fast Algorithm. Chapter 4. Wavelet Families. Chapter 5. Finding and Designing a Wavelet. Chapter 6. A Short 1D Illustrated Handbook. Chapter 7. Signal Denoising and Compression. Chapter 8. Image Processing with Wavelets. Chapter 9. An Overview of Applications. Appendix: The EZW Algorithm. Bibliography. Index.

Continuous-time fractional ARMA processes

The field of discrete-time fractional ARMA processes is now of longstanding interest. However, to the best of the authors knowledge, continuous time fractional ARMA processes have not yet been defined. This paper defines such a family, and proves several probabilistic results concerning the memory of these processes and the regularity properties of their sample functions.

Long Memory with Seasonal Effects

This review is devoted to stationary discrete time second order processes whose covariance asymptotically behaves like an hyperbolically damped oscillating sequence. We present the two main ways of generating parametric models of this type. Then we gather some results concerning the influence of seasonality on the classical limit theorems. Finally, we present a simulation method which we use to try a semi parametric estimation procedure adapted from the non seasonal situation.

Clustering signals using wavelets

A wavelet-based procedure for clustering signals is proposed. It combines an individual signal preprocessing by wavelet denoising, a dimensionality reduction step by wavelet compression and a classical clustering strategy applied to a suitably chosen set of wavelet coefficients. The ability of wavelets to cope with signals of arbitrary or time-dependent regularity as well as to concentrate signal energy in few large coefficients, offers a useful tool to carry out both significant noise reduction and efficient compression. A simulated example and an electrical dataset are considered to illustrate the value of introducing wavelets for clustering such complex data.

Micronde: a Matlab Wavelet Toolbox for Signals and Images

The purpose of this paper is to present Micronde, a Matlab wavelet and wavelet packet toolbox for signals and images. Micronde’s capabilities and organization are described and its use both in command line and interface mode are illustrated. Real or synthetic signals as well as images are used to present wavelet-based analysis, de-noising and compression.

Linear distribution processes

In this paper, we propose a generalization of continuous-time processed defined by X t = ∫ f ( t − s ) d W s , to the case of f being a distribution. We give a necessary and sufficient condition for f , such that the obtained process is a second order distribution process. We study the moments and the regularity of these processes. In addition, we investigate a generalization to processes with stationary increments.