The goal of this dissertation is to provide a construction method for dilation-dorthonormal wavelets in [special characters omitted]. We use multiplicity theory and Generalized Multiresolution Analyses (GMRAs) to develop necessary and sufficient conditions for building dilation-…
In the early 80's, the convergence of research in engineering (signal processing), mathematics (harmonic analysis), and physics (quantum mechanics) gave birth to wavelet theory. At the same time, Gilles Deslauriers and Serge Dubuc (and others) came up with iterative interpolatio…
Reducing Bit Error Ratio (BER) and improving performance of modern coherent optical communication system is a significant issue. As the distance travelled by the information signal increases, the bit error ratio will degrade. Machine learning techniques (ML) have been used in ap…
The fracture of brittle materials is of utmost importance for civil engineering and seismology applications. A different approach towards the aim of early identification of fracture and the prediction of failure before it occurs is attempted in this work. Laboratory experiments …
Nowadays data assimilation is an essential component of any effective environmental prediction system. Environmental prediction models are, indeed, initial value problems and their forecast skills highly depend on the quality of their initialization. Data assimilation (DA) seeks…
This thesis examines the issue of detecting components or features within time series data in automatic procedures. We begin by introducing the concept of Wavelets and briefly show their usage as a tool for detection. This leads to our first contribution which is a novel method …
"Barbara Burke Hubbard begins her examination of wavelets with the story of the development of Fourier analysis, the essential underpinning for telephones, x-ray machines, and computers. Without any dizzying technical or mathematical detail she describes the more recent, meteori…
A bestseller in its first edition, Wavelets and Other Orthogonal Systems: Second Edition has been fully updated to reflect the recent growth and development of this field, especially in the area of multiwavelets. The authors have incorporated more examples and numerous illustrat…