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Intro; Foreword; Preface; Contents; About the Authors; 1 Preliminaries; 1.1 Introduction; 1.2 Basic Concepts of Functional Analysis; 1.3 A Short Tour of Wavelet Transform; 1.3.1 Fourier Transform; 1.3.2 Wavelet Transform; 1.3.3 Continuous Wavelet Transform; 1.3.4 Discrete Wavelet Transform; 1.4 Haar Scaling Functions and Function Space; 1.4.1 Translation and Scaling of (t); 1.4.2 Orthogonality of Translates of (t); 1.4.3 Function Space V0; 1.4.4 Finer Haar Scaling Functions; 1.4.5 Nested Space; 1.4.6 Haar Wavelet Function; 1.4.7 Scaled Haar Wavelet Functions
3.3 Convolution Bounds and Convergence of Wavelet Packet Series4 Function Spaces and Wavelet Packets; 4.1 Introduction; 4.2 Lebesgue Spaces Lp(mathbbR) and Wavelet Packets; 4.3 Hardy Space calH1(mathbbR) and Wavelet Packets; 4.4 Sobolev Spaces Lp,s (mathbbR) and Wavelet Packets; 5 Applications in Signal Processing; 5.1 Introduction; 5.2 Applications of Wavelets in Speech Denoising; 5.2.1 Speech Signal Processing; 5.2.2 Noise Reduction in Speech Signal Using Thresholding in Wavelet Transform Domain; 5.2.3 Estimation of Speech Signal in the Presence of White Noise Using Wavelet Transform
5.3 Applications of Wavelet Packets in Speech Denoising5.3.1 Denoising of Speech Signal by Using Wavelet Packet Transform; 5.3.2 Selection of Optimal Decomposition Level Based on Entropy for Speech Denoising Using Wavelet Packets; 5.3.3 Thresholding Method for Denoising Speech Signal Using Wavelet Packet Transform; 5.4 Applications of Wavelets in Biomedical Signals; 5.4.1 ECG Signal Characteristics; 5.4.2 Performance Comparison of Wavelet Threshold Estimators for ECG Signal Denoising; 5.4.3 Denoising of ECG Signal Using Wavelet Transform
5.5 Applications of Wavelet Packets in ECG Signal Denoising5.5.1 Wavelet Packet Thresholding Method for Denoising ECG Signal; 5.5.2 Baseline Drift Correction in ECG Signal Using Wavelet Packets Transform; 6 Applications in Image Processing; 6.1 Introduction; 6.2 Applications of Wavelets in Image Denoising; 6.3 Applications of Wavelet Packets in Image Denoising; References; ; Index
3.3 Convolution Bounds and Convergence of Wavelet Packet Series4 Function Spaces and Wavelet Packets; 4.1 Introduction; 4.2 Lebesgue Spaces Lp(mathbbR) and Wavelet Packets; 4.3 Hardy Space calH1(mathbbR) and Wavelet Packets; 4.4 Sobolev Spaces Lp,s (mathbbR) and Wavelet Packets; 5 Applications in Signal Processing; 5.1 Introduction; 5.2 Applications of Wavelets in Speech Denoising; 5.2.1 Speech Signal Processing; 5.2.2 Noise Reduction in Speech Signal Using Thresholding in Wavelet Transform Domain; 5.2.3 Estimation of Speech Signal in the Presence of White Noise Using Wavelet Transform
5.3 Applications of Wavelet Packets in Speech Denoising5.3.1 Denoising of Speech Signal by Using Wavelet Packet Transform; 5.3.2 Selection of Optimal Decomposition Level Based on Entropy for Speech Denoising Using Wavelet Packets; 5.3.3 Thresholding Method for Denoising Speech Signal Using Wavelet Packet Transform; 5.4 Applications of Wavelets in Biomedical Signals; 5.4.1 ECG Signal Characteristics; 5.4.2 Performance Comparison of Wavelet Threshold Estimators for ECG Signal Denoising; 5.4.3 Denoising of ECG Signal Using Wavelet Transform
5.5 Applications of Wavelet Packets in ECG Signal Denoising5.5.1 Wavelet Packet Thresholding Method for Denoising ECG Signal; 5.5.2 Baseline Drift Correction in ECG Signal Using Wavelet Packets Transform; 6 Applications in Image Processing; 6.1 Introduction; 6.2 Applications of Wavelets in Image Denoising; 6.3 Applications of Wavelet Packets in Image Denoising; References; ; Index