This book provides an overview of the theory and practice of continuous and discrete wavelet transforms. Divided into seven chapters, the first three chapters of the book are introductory, describing the various forms of the wavelet transform and their computation, while the remaining chapters are devoted to applications in fluids, engineering, medicine and miscellaneous areas. Each chapter is well introduced, with suitable examples to demonstrate key concepts. Illustrations are included where appropriate, thus adding a visual dimension to the text. A noteworthy feature is the inclusion, at the end of each chapter, of a list of further resources from the academic literature which the interested reader can consult. The first chapter is purely an introduction to the text. The treatment of wavelet transforms begins in the second chapter, with the definition of what a wavelet is. The chapter continues by defining the continuous wavelet transform and its inverse and a description of how it may be used to interrogate signals. The continuous wavelet transform is then compared to the short-time Fourier transform. Energy and power spectra with respect to scale are also discussed and linked to their frequency counterparts. Towards the end of the chapter, the two-dimensional continuous wavelet transform is introduced. Examples of how the continuous wavelet transform is computed using the Mexican hat and Morlet wavelets are provided throughout. The third chapter introduces the discrete wavelet transform, with its distinction from the discretized continuous wavelet transform having been made clear at the end of the second chapter. In the first half of the chapter, the logarithmic discretization of the wavelet function is described, leading to a discussion of dyadic grid scaling, frames, orthogonal and orthonormal bases, scaling functions and multiresolution representation. The fast wavelet transform is introduced and its computation is illustrated with an example using the Haar wavelet. The second half of the chapter groups together miscellaneous points about the discrete wavelet transform, including coefficient manipulation for signal denoising and smoothing, a description of Daubechies' wavelets, the properties of translation invariance and biorthogonality, the two-dimensional discrete wavelet transforms and wavelet packets. The fourth chapter is dedicated to wavelet transform methods in the author's own specialty, fluid mechanics. Beginning with a definition of wavelet-based statistical measures for turbulence, the text proceeds to describe wavelet thresholding in the analysis of fluid flows. The remainder of the chapter describes wavelet analysis of engineering flows, in particular jets, wakes, turbulence and coherent structures, and geophysical flows, including atmospheric and oceanic processes. The fifth chapter describes the application of wavelet methods in various branches of engineering, including machining, materials, dynamics and information engineering. Unlike previous chapters, this (and subsequent) chapters are styled more as literature reviews that describe the findings of other authors. The areas addressed in this chapter include: the monitoring of machining processes, the monitoring of rotating machinery, dynamical systems, chaotic systems, non-destructive testing, surface characterization and data compression. The sixth chapter continues in this vein with the attention now turned to wavelets in the analysis of medical signals. Most of the chapter is devoted to the analysis of one-dimensional signals (electrocardiogram, neural waveforms, acoustic signals etc.), although there is a small section on the analysis of two-dimensional medical images. The seventh and final chapter of the book focuses on the application of wavelets in three seemingly unrelated application areas: fractals, finance and geophysics. The treatment on wavelet methods in fractals focuses on stochastic fractals with a short section on multifractals. The treatment on finance touches on the use of wavelets by other authors in studying stock prices, commodity behaviour, market dynamics and foreign exchange rates. The treatment on geophysics covers what was omitted from the fourth chapter, namely, seismology, well logging, topographic feature analysis and the analysis of climatic data. The text concludes with an assortment of other application areas which could only be mentioned in passing. Unlike most other publications in the subject, this book does not treat wavelet transforms in a mathematically rigorous manner but rather aims to explain the mechanics of the wavelet transform in a way that is easy to understand. Consequently, it serves as an excellent overview of the subject rather than as a reference text. Keeping the mathematics to a minimum and omitting cumbersome and detailed proofs from the text, the book is best-suited to those who are new to wavelets or who want an intuitive understanding of the subject. Such an audience may include graduate students in engineering and professionals and researchers in engineering and the applied sciences.

The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance

Structural vibrations caused by a flowing fluid. Whenever a structure is exposed to a flowing fluid,…

Flow-induced vibration

Combined electrocoagulation processes as a novel approach for enhanced pollutants removal: A state-of-the-art review

Formation and mechanisms of nano-metal oxide-biochar composites for pollutants removal: A review

A magnetically coupled bistable piezoelectric harvester for underwater energy harvesting

There are many different industrial wastewater containing heavy metals that contribute to environmental pollution and raw agricultural waste is an effective adsorbent for the removal of heavy metals. The adsorption behavior of pistachio hull powder (PHP) as a low-cost adsorbent, with respect to nickel (II) ions, has been studied in order to consider its application to the purification of metal finishing wastewater. In this work, adsorption of nickel on pistachio hull has been studied by batch techniques. The adsorption depends on the process time, the pH of the solution, initial concentration of metals and the adsorbent concentration in the suspension. The kinetics of adsorption were relatively fast, reaching equilibrium for less than 60 minutes. Kinetic and isotherm modeling studies demonstrated that the experimental data best fit a pseudo-second order and Freundlich model, respectively. The maximum Langmuir adsorption capacity was 14 mg/g. The optimum pH required for maximum adsorption was found to be 4-6. The initial concentration of the adsorbate and the concentration of pistachio hull strongly affect the process. No influence of particle size was evidenced. A degree of adsorption higher than 75% can be achieved for nickel (II) ions.

/pdf/biosorption-of-nickel-ii-from-aqueous-solutions-onto-2d0n9x3zkn.pdf

Biosorption of Nickel (II) from Aqueous Solutions onto Pistachio Hull Waste as a Low-Cost Biosorbent

Flow induced vibrations of a sharp edge square cylinder in the wake of a circular cylinder

Finding the Socially Optimal Solution for California's Sacramento-San Joaquin Delta Problem

Marine hydrokinetic energy harvesting performance of diamond and square oscillators in tandem arrangements

This in-water experimental study deals with the effects of the after-body on the FIV response of round and sharp edge cylinders. Different circular, square, diamond, and right-angle isosceles trian...

Seyed Taghi Omid Naeeni

Papers

Biosorption of Nickel (II) from Aqueous Solutions onto Pistachio Hull Waste as a Low-Cost Biosorbent

Flow induced vibrations of a sharp edge square cylinder in the wake of a circular cylinder

Finding the Socially Optimal Solution for California's Sacramento-San Joaquin Delta Problem

Marine hydrokinetic energy harvesting performance of diamond and square oscillators in tandem arrangements

Effects of after-body on the FIV of a right-angle triangular cylinder in comparison to circular, square, and diamond cross-sections