Construction of Wavelets in Frequency Domain
摘要
This chapter presents the construction of wavelets in the frequency domain. It begins with a discussion on wavelet parameters, which define the essential properties of wavelets including compact support, vanishing moments, and regularity conditions. The parametric design of orthogonal wavelets is then introduced, where frequency domain formulations are employed to ensure orthogonality, perfect reconstruction, and spectral localization. The design of matched wavelets is explored, emphasizing the adaptation of wavelet functions to specific signal structures for improved representation and feature extraction.