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Surface texture is one of the most critical factors and important functionality indicators in the performance of high precision and nanoscale devices and components. The functions that have been identified in various studies include wear, friction, lubrication, corrosion, fatigue, coating, paintability, etc. [1-3]. It is also reported that the wear rates of surfaces in operational service is determined by roughness, waviness and the multi-scalar topographic features of a surface, such as random peaks/pits and ridges/valleys. These functional topographical features will impact directly on wear mechanics and physical properties of a whole system, such as hip joint replacement system in bioengineering [4-9]. For example, during functional operation of interacting surfaces, peaks and ridges will act as sites of high contact stresses and abrasion; consequently wear particles and debris will be generated by such surface topographical features, whereas the pits and valleys will affect the lubrication and fluid retention properties. In this situation, a vitally important consideration for functional characterisation must be the appropriate separation of the different components of surfaces, which is not only to extract roughness, waviness and form error, but should also be extended to all multi-scalar topographical events over surfaces.
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This book captures the essence of the current state of research in wavelet analysis and its applications, and identifies the changes and opportunities - both current and future in the field. Distinguished researchers such as Prof John Daugman from Cambridge University and Prof Victor Wickerhauser from Washington University present their research papers.
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Wavelet analysis and its applications have been one of the fastest- growing research areas in the past several years. Wavelet theory has been employed in numerous fields and applications, such as signal and image processing, communication systems, biomedical imaging, radar, and air acoustics.
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Wavelet Transform and Complexity presents high-level content on the fascinating field of wavelet transform and its applications in real-world phenomena. Divided into two parts, Analysis and Real-World Applications, the book describes the application of the wavelet method to several interesting complex systems across various disciplines. The book is designed for students, postdocs, and researchers interested in studying the wavelet method and its applications.
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Today, more sophisticated techniques are necessary for spectral analysis, reconstruction, restoration of signals, their digital and analogic processing, specialized signal diagnostics, and short intervals with occurrences that require greater speed and precision. As the frequency domain of the wavelet transform gets more detailed and considerably more specific in various applications, it necessitates specialized scholarly attention in its many forms and relationships with other transforms with special functions. For example, using the wavelet transform with special functions can prove valuable in creating and designing special signal filters or the interphase between reception-emission devices with specialized sensors for medical use. In quantum phenomena, its corresponding version of the wavelet transform is instrumental in the spectral study of particles and their correlation. Therefore, using specialists' and experts' views, this book delves into an exposition on spectral analysis, restoring, monitoring, and signal processing, as well as essential applications required in waveguides and for the improvement of medical images, proving the wavelet transform to be helpful in resolution analysis in time-frequency, with an emphasis on different methods of the calculus using FFT and DSTFT. This book has been divided into four sections covering all the abovementioned subjects.
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Wavelet analysis has gained recognition as a useful tool for analyzing time-frequency, and it plays an important role in signal and information processing. This book captures the essence of the state of the art in wavelet analysis and active media technology.
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The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID.
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This book gives a comprehensive overview of both the fundamentals of wavelet analysis and related tools, and of the most active recent developments towards applications. It offers a state-of-the-art in several active areas of research where wavelet ideas, or more generally multiresolution ideas have proved particularly effective. The main applications covered are in the numerical analysis of PDEs, and signal and image processing. Recently introduced techniques such as Empirical Mode Decomposition (EMD) and new trends in the recovery of missing data, such as compressed sensing, are also present
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