From Fourier analysis to wavelets [electronic resource]

• 作者： Gomes, Jonas.
• 其他作者：
  • Velho, Luiz.
  • SpringerLink (Online service)
• 其他題名：
  • IMPA monographs ;
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： IMPA monographs ;v.3
• 主題： Wavelets (Mathematics) , Fournier analysis. , Mathematics , Fourier analysis , Abstract Harmonic Analysis. , Signal, Image and Speech Processing.
• ISBN： 9783319220758 (electronic bk.) 、 9783319220741 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Introduction -- Function Representation and Reconstruction -- The Fourier Transform -- Windowed Fourier Transform -- The Wavelet Transform -- Multiresolution Representation -- The Fast Wavelet Transform -- Filter Banks and Multiresolution -- Constructing Wavelets -- Wavelet Design -- Orthogonal Wavelets -- Biorthogonal Wavelets -- Directions and Guidelines -- Appendices.
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• 摘要註: This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
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