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BL
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| Record Number
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889568
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| Main Entry
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Ahmad, Khalil, (Mathematician)
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| Title & Author
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Wavelet packets and their statistical applications /\ Khalil Ahmad, Abdullah.
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| Publication Statement
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Singapore :: Springer,, 2018.
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| Series Statement
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Forum for interdisciplinary mathematics,
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| Page. NO
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1 online resource
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| ISBN
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9789811302688
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: 9811302685
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9789811302671
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9811302677
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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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.
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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.
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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.
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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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| Abstract
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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.--
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| Subject
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Wavelets (Mathematics)
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| Subject
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MATHEMATICS-- Calculus.
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MATHEMATICS-- Mathematical Analysis.
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Wavelets (Mathematics)
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Mathematics.
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Applications of Mathematics.
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Functional Analysis.
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Numerical Analysis.
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Signal, Image and Speech Processing.
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| Subject
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Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
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| Dewey Classification
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515/.2433
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| LC Classification
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QA403.3
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| Added Entry
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Abdullah
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