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Foundation and Core Wavelet Theory

Foundation and Core Wavelet Theory

Concepts, Mathematics, and Python Foundations

This volume introduces the foundations and core principles of wavelet theory, providing a structured and rigorous entry point into multiscale analysis. It develops the essential mathematical concepts underlying wavelet representations while emphasizing intuition and interpretability. Rather than focusing on isolated algorithms, the book explains why wavelet methods work and how their assumptions influence real-world analysis.

Designed as a foundational reference, this volume prepares readers for applied and computational work by establishing a clear conceptual framework. It is intended for researchers, engineers, and applied scientists who seek both mathematical rigor and practical understanding in modern signal and data analysis.

This volume provides:

  • Mathematical foundations of wavelet theory
  • Scaling functions and orthonormal wavelet bases
  • Multiresolution Analysis (MRA) framework
  • 1D, 2D, and nD Discrete Wavelet Transform (DWT)
  • Stationary Wavelet Transform (SWT)
  • Wavelet Packet Transform (WPT)
  • PyWavelets implementation strategies
  • Reproducible scientific Python workflows
  • Visualization and interpretation of wavelet coefficients
  • Foundations for production-ready analytical pipelines
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Publication Details

About the Author

Shouke Wei

Shouke Wei, PhD, is a researcher, scientist, and entrepreneur specializing in intelligent IoT systems, robotics, big data analytics, modeling and forecasting, early-warning systems, and edge computing. With academic and industry experience across Europe, North America, and Asia, Dr. Wei is recognized for bridging advanced theory with real-world, production-ready systems.

Dr. Wei earned his Ph.D. in Environmental and Resource Management from the Department of Environmental Informatics at Brandenburg University of Technology Cottbus–Senftenberg (Germany). He conducted postdoctoral research at the Swiss Federal Institute of Aquatic Science and Technology (Eawag), where he also served as a doctoral supervisor, and held research positions at the University of British Columbia (Canada). He has held distinguished and adjunct professorships at multiple institutions, including Yantai University, Ludong University, and Jining University. He has served as a graduate supervisor and distinguished professor in computer science, control engineering, and applied mathematics.

Dr. Wei’s work focuses on making advanced computational methods—particularly wavelet-based signal processing—accessible, practical, and impactful for researchers and practitioners worldwide. [More About the Author]

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