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140122 ||| eng |
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|a 9781461200970
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|a Debnath, Lokenath
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| 245 |
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|a Wavelet Transforms and Their Applications
|h Elektronische Ressource
|c by Lokenath Debnath
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| 250 |
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|a 1st ed. 2002
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| 260 |
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|a Boston, MA
|b Birkhäuser
|c 2002, 2002
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| 300 |
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|a XV, 565 p
|b online resource
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| 505 |
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|a 1 Brief Historical Introduction -- 1.1 Fourier Series and Fourier Transforms -- 1.2 Gabor Transforms -- 1.3 The Wigner-Ville Distribution and Time-Frequency Signal Analysis -- 1.4 Wavelet Transforms -- 1.5 Wavelet Bases and Multiresolution Analysis -- 1.6 Applications of Wavelet Transforms -- 2 Hilbert Spaces and Orthonormal Systems -- 2.1 Introduction -- 2.2 Normed Spaces -- 2.3 The Lp Spaces -- 2.4 Generalized Functions with Examples -- 2.5 Definition and Examples of an Inner Product Space -- 2.6 Norm in an Inner Product Space -- 2.7 Definition and Examples of a Hilbert Space -- 2.8 Strong and Weak Convergences -- 2.9 Orthogonal and Orthonormal Systems -- 2.10 Properties of Orthonormal Systems -- 2.11 Trigonometric Fourier Series -- 2.12 Orthogonal Complements and the Projection Theorem -- 2.13 Linear Funtionals and the Riesz Representation Theorem -- 2.14 Separable Hilbert Spaces -- 2.15 Linear Operators on Hilbert Spaces -- 2.16 Eigenvalues and Eigenvectors of an Operator --
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|a 9.4 Farge’s Wavelet Transform Analysis of Turbulence -- 9.5 Adaptive Wavelet Method for Analysis of Turbulent Flows -- 9.6 Meneveau’s Wavelet Analysis of Turbulence -- Answers and Hints for Selected Exercises
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|a 2.17 Exercises -- 3 Fourier Transforms and Their Applications -- 3.1 Introduction -- 3.2 Fourier Transforms in L1 (R) -- 3.3 Basic Properties of Fourier Transforms -- 3.4 Fourier Transforms in L2 (R) -- 3.5 Poisson’s Summation Formula -- 3.6 The Shannon Sampling Theorem and Gibbs’s Phenomenon -- 3.7 Heisenberg’s Uncertainty Principle -- 3.8 Applications of Fourier Transforms in Mathematical Statistics -- 3.9 Applications of Fourier Transforms to Ordinary Differential Equations -- 3.10 Solutions of Integral Equations -- 3.11 Solutions of Partial Differential Equations -- 3.12 Applications of Multiple Fourier Transforms to Partial Differential Equations -- 3.13 Construction of Green’s Functions by the Fourier Transform Method -- 3.14 Exercises -- 4 The Gabor Transform and Time-Frequency Signal Analysis -- 4.1 Introduction -- 4.2Classification of Signals and the Joint Time-Frequency Analysis of Signals -- 4.3 Definition and Examples of the Gabor Transforms --
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|a 6.2 Continuous Wavelet Transforms and Examples -- 6.3 Basic Properties of Wavelet Transforms -- 6.4 The Discrete Wavelet Transforms -- 6.5 Orthonormal Wavelets -- 6.6 Exercises -- 7 Multiresolution Analysis and Construction of Wavelets -- 7.1 Introduction -- 7.2 Definition of Multiresolution Analysis and Examples -- 7.3 Properties of Scaling Functions and Orthonormal Wavelet Bases -- 7.4 Construction of Orthonormal Wavelets -- 7.5 Daubechies’ Wavelets and Algorithms -- 7.6 Discrete Wavelet Transforms and Mallat’s Pyramid Algorithm -- 7.7 Exercises -- 8 Newland’s Harmonic Wavelets -- 8.1 Introduction -- 8.2 Harmonic Wavelets -- 8.3 Properties of Harmonic Scaling Functions -- 8.4 Wavelet Expansions andParseval’s Formula -- 8.5 Concluding Remarks -- 8.6 Exercises -- 9 Wavelet Transform Analysis of Turbulence -- 9.1 Introduction -- 9.2 Fourier Transforms in Turbulence and the Navier-Stokes Equations -- 9.3 Fractals, Multifractals, and Singularities in Turbulence --
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|a 4.4 Basic Properties of Gabor Transforms -- 4.5 Frames and Frame Operators -- 4.6 Discrete Gabor Transforms and the Gabor Representation Problem -- 4.7 The Zak Transform and Time-Frequency Signal Analysis -- 4.8 Basic Properties of Zak Transforms -- 4.9 Applications of Zak Transforms and the Balian-Low Theorem -- 4.10 Exercises -- 5 The Wigner-Ville Distribution and Time-Frequency Signal Analysis -- 5.1 Introduction -- 5.2 Definitions and Examples of the Wigner-Ville Distribution -- 5.3 Basic Properties of the Wigner-Ville Distribution -- 5.4 The Wigner-Ville Distribution of Analytic Signals and Band-Limited Signals -- 5.5 Definitions and Examples of the Woodward Ambiguity Functions -- 5.6 Basic Properties of Ambiguity Functions -- 5.7 The Ambiguity Transformation and Its Properties -- 5.8 Discrete Wigner-Ville Distributions -- 5.9 Cohen’s Class of Time-Frequency Distributions -- 5.10 Exercises -- 6 Wavelet Transforms and Basic Properties -- 6.1 Introduction --
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| 653 |
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|a Functional analysis
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| 653 |
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|a Functional Analysis
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| 653 |
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|a Electrical and Electronic Engineering
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| 653 |
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|a Electrical engineering
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| 653 |
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|a Signal, Speech and Image Processing
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| 653 |
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|a Applications of Mathematics
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| 653 |
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|a Signal processing
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| 653 |
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|a Mathematics
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| 041 |
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|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 028 |
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|a 10.1007/978-1-4612-0097-0
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| 856 |
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|u https://doi.org/10.1007/978-1-4612-0097-0?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 621.3
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| 520 |
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|a Overview Historically, the concept of "ondelettes" or "wavelets" originated from the study of time-frequency signal analysis, wave propagation, and sampling theory. One of the main reasons for the discovery of wavelets and wavelet transforms is that the Fourier transform analysis does not contain the local information of signals. So the Fourier transform cannot be used for analyzing signals in a joint time and frequency domain. In 1982, Jean MorIet, in collaboration with a group of French engineers, first introduced the idea of wavelets as a family of functions constructed by using translation and dilation of a single function, called the mother wavelet, for the analysis of nonstationary signals. However, this new concept can be viewed as the synthesis of various ideas originating from different disciplines including mathematics (Calder6n-Zygmund operators and Littlewood-Paley theory), physics (coherent states in quantum mechanics and the renormalization group), and engineering (quadratic mirror filters, sideband coding in signal processing, and pyramidal algorithms in image processing). Wavelet analysis is an exciting new method for solving difficult problems in mathematics, physics, and engineering, with modern applications as diverse as wave propagation, data compression, image processing, pattern recognition, computer graphics, the detection of aircraft and submarines, and improvement in CAT scans and other medical image technology. Wavelets allow complex information such as music, speech, images, and patterns to be decomposed into elementary forms, called the fundamental building blocks, at different positions and scales and subsequently reconstructed with high precision
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