This first volume, Foundations and Core Wavelet Theory: Concepts, Mathematics, and Python Foundations, establishes the theoretical and computational groundwork for the volumes that follow. It introduces the fundamental principles of wavelet analysis, including core mathematical constructs and their relationship to classical signal-processing methods. Building upon this foundation, the volume presents essential discrete wavelet techniques-implemented using the PyWavelets library-while maintaining a consistent emphasis on clarity, structure, and reproducibility.
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