Wavelet Transform and Fractional Fourier Transform Theory and Applications

Author: Ran Qiwen
Publisher:
Publish Date: 2001-01-01
Features: This book focuses on introducing the basic methods, fundamental ideas, essential tools, and several typical application areas of wavelet analysis. The content includes a comparison between wavelet analysis and Fourier analysis, integral wavelet transform, orthogonal multi-scale analysis, orthogonal wavelets, compactly supported orthogonal wavelets, decomposition and synthesis algorithms for wavelets and wavelet packets, time-frequency analysis, and corresponding algorithms. Considering that the fractional Fourier transform, an improved form of the Fourier transform that has only developed in recent years, is also a type of Fourier transform, this book introduces the development status and basic theory of the fractional Fourier transform in the last three chapters. For the convenience of readers, the discrete algorithms of the fractional Fourier transform are discussed in detail in matrix form, with the hope of being helpful to readers when they understand and use the fractional Fourier transform.