From Fourier Analysis to Wavelets

“The authors present a short textbook about thefundamentals of Fourier analysis (such as Fourier series, Fourier transform,and windowed Fourier transform) and wavelet theory (such as continuous/discretewavelet transforms, multiresolution analysis, decomposition/reconstructionalgorithms, and construction of orthogonal/biorthogonal wavelets) with emphasison the underlying ideas. … This textbook is mainly written for students incomputer science, physics, and engineering.” (Manfred Tasche, zbMATH, Vol.1325.42001, 2016)

• 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.