Wavelets and Their Recent Applications
Jamkhongam Touthang · 2025
Wavelet analysis addresses the limitations of Fourier analysis. Wavelet systems are vital tools for series representations of functions in Hilbert spaces. They have found applications in various fields, and ongoing research and technological advancements continue to expand their use. The chapter provides an overview of wavelet systems and discusses their mathematical properties and recent applications in fields where research is still in its early stages. Recent applications of wavelets include neural networks, digital image processing, data analysis, biomedical signal processing, internet voting, geophysical signal processing, cyber security, and fingerprints. Despite their successful applications in many areas, wavelets have limitations, prompting consideration of alternatives such as Gabor systems in certain scenarios. We present some important aspects of Gabor systems that make them effective in various applications.