عنوان

Wavelet packets and their statistical applications /

9789811302688

9811302685

9789811302671

9811302677

Wavelet packets and their statistical applications /

[Book]

Khalil Ahmad, Abdullah.

Singapore :

Springer,

2018.

1 online resource

Forum for interdisciplinary mathematics,

2364-6748

Includes bibliographical references and index.

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.

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This book presents the basic concepts of functional analysis, wavelet analysis and thresholding. It begins with an elementary chapter on preliminaries such as basic concepts of functional analysis, a brief tour of the wavelet transform, Haar scaling functions and function space, wavelets, symlets wavelets and coiflets wavelets. In turn, Chapters 2 and 3 address the construction of wavelet packets, selected results on wavelet packets, band-limited wavelet packets, characterisations of wavelet packets, multiresolution analysis (MRA) wavelet packets, pointwise convergence, the convergence of wavelet packet series and convolution bounds. Chapter 4 discusses characterisations of function spaces like Lebesgue spaces, Hardy spaces and Sobolev spaces in terms of wavelet packets, while Chapter 5 is devoted to applications of wavelets and wavelet packets in speech denoising and biomedical signals. In closing, Chapter 6 highlights applications of wavelets and wavelet packets in image denoising.--

Springer Nature

com.springer.onix.9789811302688

Wavelet packets and their statistical applications.

9789811302671

Wavelets (Mathematics)

Applications of Mathematics.

Functional Analysis.

Mathematics.

Numerical Analysis.

Signal, Image and Speech Processing.

Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.

MATHEMATICS-- Calculus.

MATHEMATICS-- Mathematical Analysis.

Wavelets (Mathematics)

MAT-- 005000

MAT-- 034000

PBKF

Ahmad, Khalil, (Mathematician)

Abdullah

20200823223601.0

pn

[Book]

Y