## A First Course in Wavelets with Fourier AnalysisThis book fills the gap between volumes on wavelets that are either too advanced (in terms of mathematical background required) or that contain too little mathematical theory underlying wavelets. It presents most of the theory underlying Fourier analysis and wavelets in a clear and comprehensive fashion-- without requiring advanced background in real analysis. Provides a careful balance between theory and practical algorithms, and features a clear presentation of applications to digital signal processing--e.g., data compression, digital filtering and singularity detection. Includes illustrations and MATLAB code used in many of the algorithms. Inner Product Spaces. Fourier Series. The Fourier Transform. Discrete Fourier Analysis. Wavelet Analysis. Multiresolution Analysis. The Daubechies Wavelets. For anyone interested in Wavelets and Fourier Analysis. |

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### Contents

Fourier Series | 37 |

The Fourier Transform | 91 |

Discrete Fourier Analysis | 131 |

Copyright | |

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### Common terms and phrases

adjoint approximation Chapter compact support complex compute constructed converges uniformly cosine Daubechies wavelets decomposition algorithm decomposition and reconstruction defined definition differentiable discontinuous discrete Fourier transform equal equation equivalent Example Exercise fast Fourier transform fc=i filter finite number following theorem formula Fourier coefficients Fourier series frequency components function f(x Gibbs phenomenon given in Figure given in Theorem graph Haar scaling function Haar wavelets inequality inner product space integral inverse ip(x iterative J-oo L2-norm least squares linear combination linear operator linear predictive coding Matlab matrix multiplications multiresolution analysis nodes nonzero obtain odd function orthogonal projection orthonormal basis orthonormality condition piecewise Plot polynomial preceding proof of Theorem properties real number reconstruction algorithms Riemann-Lebesgue lemma sampling sequence sin(fcx sine step function subspace Theorem 1.2 values vector wavelet coefficients Z-transform zero