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| What is this book all about? | |
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| Mathematical Preliminary | |
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| Linear Spaces | |
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| Vectors and Vector Spaces | |
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| Basis Functions, Orthogonality and Biothogonality | |
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| Local Basis and Riesz Basis | |
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| Discrete Linear Normed Space | |
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| Approximation by Orthogonal Projection | |
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| Matrix Algebra and Linear Transformation | |
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| Digital Signals | |
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| Exercises | |
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| References | |
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| Fourier Analysis | |
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| Fourier Series | |
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| Rectified Sine Wave | |
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| Fourier Transform | |
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| Properties of Fourier Transform | |
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| Examples of Fourier Transform | |
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| Poisson's Sum and Partition of ZUnity | |
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| Sampling Theorem | |
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| Partial Sum and Gibb's Phenomenon | |
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| Fourier Analysis of Discrete-Time Signals | |
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| Discrete Fourier Transform (DFT) | |
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| Exercise | |
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| References | |
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| Time-Frequency Analysis | |
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| Window Function | |
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| Short-Time Fourier Transform | |
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| Discrete Short-Time Fourier Transform | |
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| Discrete Gabor Representation | |
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| Continuous Wavelet Transform | |
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| Discrete Wavelet Transform | |
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| Wavelet Series | |
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| Interpretations of the Time-Frequency Plot | |
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| Wigner-Ville Distribution | |
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| Properties of Wigner-Ville Distribution | |
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| Quadratic Superposition Principle | |
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| Ambiguity Function | |
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| Exercise | |
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| Computer Programs | |
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| References | |
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| Multiresolution Anaylsis | |
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| Multiresolution Spaces | |
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| Orthogonal, Biothogonal, and Semiorthogonal Decomposition | |
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| Two-Scale Relations | |
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| Decomposition Relation | |
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| Spline Functions and Properties | |
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| Mapping a Function into MRA Space | |
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| Exercise | |
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| Computer Programs | |
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| References | |
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| Construction of Wavelets | |
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| Necessary Ingredients for Wavelet Construction | |
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| Construction of Semiorthogonal Spline Wavelets | |
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| Construction of Orthonormal Wavelets | |
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| Orthonormal Scaling Functions | |
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| Construction of Biothogonal Wavelets | |
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| Graphical Display of Wavelet | |
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| Exercise | |
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| Computer Programs | |
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| References | |
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| DWT and Filter Bank Algorithms | |
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| Decimation and Interpolation | |
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| Signal Representation in the Approximation Subspace | |
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| Wavelet Decomposition Algorithm | |
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| Reconstruction Algorithm | |
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| Change of Bases | |
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| Signal Reconstruction in Semiorthogonal Subspaces | |
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| Examples | |
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| Two-Channel Perfect Reconstruction Filter Bank | |
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| Polyphase Representation for Filter Banks | |
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| Comments on DWT and PR Filter Banks | |
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| Exercise | |
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| Computer Program | |
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| References | |
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| Special Topics in Wavelets and Algorithms | |
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| Fast Integral Wavelet Transform | |
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| Ridgelet Transform | |
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| Curvelet Transform | |
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| Complex Wavelets | |
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| Lifting Wavelet transform | |
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| References | |
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| Digital Signal Processing Applications | |
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| Wavelet Packet | |
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| Wavelet-Packet Algorithms | |
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| Thresholding | |
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| Interference Suppression | |
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| Faulty Bearing Signature Identification | |
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| Two-Dimensional Wavelets and Wavelet Packets | |
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| Edge Detection | |
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| Image Compression | |
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| Microcalcification Cluster Detection | |