傅立叶分析和应用Fourier analysis and applications : filtering, numerical computation, wavelets

傅立叶分析和应用Fourier analysis and applications : filtering, numerical computation, wavelets

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作者: Robert D. Ryan 著 , Claude Gasquet

出版社: Oversea Publishing House

出版时间: 1998-11

版次: 1

ISBN: 9780387984858

定价: 869.00

装帧: 精装

开本: 16开

纸张: 胶版纸

页数: 442页

分类: 外文古旧书>英文书>工程技术

This applied mathematic text focuses on Fourier analysis, filters and signal analysis. Scientists and engineers are confronted by the necessity of using classical mathematics such as Fourier transforms, convolution, distribution and more recently wavelet analysis in all areas of modelling. The object of this book is two-fold - on the one hand to convey to the mathematical reader a rigorous presentation and exploration of the important applications of analysis leading to numerical calculations and on the other hand to convey to the physics reader a body of theory in which the well-known formulae find their justification. The reader will find the basic study of fundamental notions such as Lebesgue integration and theory of distribution and these permit the establishment of the following areas: Fourier analysis and convolution Filters and signal analysis time-frequency analysis (gabor transforms and wavelets) The book is aimed at engineers and scientists and contains a large number of exercises as well as selected worked out solutions. The words `Translated by Robert D Ryan' should be included in ALL promotion material regarding the book. Translator's Preface    v (2)

Preface to the French Edition    vii

Chapter Ⅰ Signals and Systems

  Lesson 1 Signals and Systems

    1.1 General considerations

    1.2 Some elementary signals

    1.3 Examples of systems

  Lesson 2 Filters and Transfer Functions

    2.1 Algebraic properties of systems

    2.2 Continuity of a system

    2.3 The filter and its transfer function

    2.4 A standard analog filter: the RC cell

    2.5 A first-order discrete filter

Chapter Ⅱ Periodic Signals

  Lesson 3 Trigonometric Signals

    3.1 Trigonometric polynomials

    3.2 Representation in since and consincs

    3.3 Orthogonality

    3.4 Exercises

  Lesson 4 Periodic Signals and Fourier Series

    4.1 The space L(2)(p)(0, a)

    4.2 The idea of approximation

    4.3 Convergence of the approximation

    4.4 Fourier coefficients of real, odd, and even functions

    4.5 Formulary

    4.6 Exercises

  Lesson 5 Pointwise Representation

    5.1 The Riemann-Lebesgue theorem

    5.2 Pointwise convergence?

    5.3 Uniform convergence of Fourier series

    5.4 Exercises

  Lesson 6 Expanding a Function in an Orthogonal Basis

    6.1 Fourier series expansions on a bounded interval

    6.2 Expansion of a function in an orthogonal basis

    6.3 Exercises

  Lesson 7 Frequencies, Spectra, and Scales

    7.1 Frequencies and spectra

    7.2 Variations on the scale

    7.3 Exercises

Chapter Ⅲ The Discrete Fourier Transform and Numerical Computations

  Lesson 8 The Discrete Fourier Transform

    8.1 Computing the Fourier coefficients

    8.2 Some properties of the discrete Fourier transform

    8.3 The Fourier transform of real data

    8.4 A relation between the exact and approximate Fourier coefficients

    8.5 Exercises

  Lesson 9 A Famous, Lightning-Fast Algorithm

    9.1 The Cooley-Tukey algorithm

    9.2 Evaluating the cost of the algorithm

    9.3 The mirror permutation

    9.4 A recursive program

    9.5 Exercises

  Lesson 10 Using a FFT for Numerical Computations

    10.1 Computing a periodic convolution

    10.2 Nonperiodic convolution

    10.3 Computations on high-order polynomials

    10.4 Polynomial interpolation and the chebyshev basis

    10.5 Exercises

Chapter Ⅳ The Lebesgue Integral

Chapter Ⅴ Spaces

Chapter Ⅵ Convolution and the Fourier Transform of Functions

Chapter Ⅶ Analog Filters

Chapter Ⅷ Distributions

Chapter Ⅹ Filters and Distributions

Chapter Ⅸ Convolution and the Fourier Transform of Distributions

Chapter Ⅺ Sampling and Discrete Filters

Chapter Ⅻ Current Trends: Time-Frequency Analysis

References

Index
内容简介:
This applied mathematic text focuses on Fourier analysis, filters and signal analysis. Scientists and engineers are confronted by the necessity of using classical mathematics such as Fourier transforms, convolution, distribution and more recently wavelet analysis in all areas of modelling. The object of this book is two-fold - on the one hand to convey to the mathematical reader a rigorous presentation and exploration of the important applications of analysis leading to numerical calculations and on the other hand to convey to the physics reader a body of theory in which the well-known formulae find their justification. The reader will find the basic study of fundamental notions such as Lebesgue integration and theory of distribution and these permit the establishment of the following areas: Fourier analysis and convolution Filters and signal analysis time-frequency analysis (gabor transforms and wavelets) The book is aimed at engineers and scientists and contains a large number of exercises as well as selected worked out solutions. The words `Translated by Robert D Ryan' should be included in ALL promotion material regarding the book.
目录:
Translator's Preface    v (2)

Preface to the French Edition    vii

Chapter Ⅰ Signals and Systems

  Lesson 1 Signals and Systems

    1.1 General considerations

    1.2 Some elementary signals

    1.3 Examples of systems

  Lesson 2 Filters and Transfer Functions

    2.1 Algebraic properties of systems

    2.2 Continuity of a system

    2.3 The filter and its transfer function

    2.4 A standard analog filter: the RC cell

    2.5 A first-order discrete filter

Chapter Ⅱ Periodic Signals

  Lesson 3 Trigonometric Signals

    3.1 Trigonometric polynomials

    3.2 Representation in since and consincs

    3.3 Orthogonality

    3.4 Exercises

  Lesson 4 Periodic Signals and Fourier Series

    4.1 The space L(2)(p)(0, a)

    4.2 The idea of approximation

    4.3 Convergence of the approximation

    4.4 Fourier coefficients of real, odd, and even functions

    4.5 Formulary

    4.6 Exercises

  Lesson 5 Pointwise Representation

    5.1 The Riemann-Lebesgue theorem

    5.2 Pointwise convergence?

    5.3 Uniform convergence of Fourier series

    5.4 Exercises

  Lesson 6 Expanding a Function in an Orthogonal Basis

    6.1 Fourier series expansions on a bounded interval

    6.2 Expansion of a function in an orthogonal basis

    6.3 Exercises

  Lesson 7 Frequencies, Spectra, and Scales

    7.1 Frequencies and spectra

    7.2 Variations on the scale

    7.3 Exercises

Chapter Ⅲ The Discrete Fourier Transform and Numerical Computations

  Lesson 8 The Discrete Fourier Transform

    8.1 Computing the Fourier coefficients

    8.2 Some properties of the discrete Fourier transform

    8.3 The Fourier transform of real data

    8.4 A relation between the exact and approximate Fourier coefficients

    8.5 Exercises

  Lesson 9 A Famous, Lightning-Fast Algorithm

    9.1 The Cooley-Tukey algorithm

    9.2 Evaluating the cost of the algorithm

    9.3 The mirror permutation

    9.4 A recursive program

    9.5 Exercises

  Lesson 10 Using a FFT for Numerical Computations

    10.1 Computing a periodic convolution

    10.2 Nonperiodic convolution

    10.3 Computations on high-order polynomials

    10.4 Polynomial interpolation and the chebyshev basis

    10.5 Exercises

Chapter Ⅳ The Lebesgue Integral

Chapter Ⅴ Spaces

Chapter Ⅵ Convolution and the Fourier Transform of Functions

Chapter Ⅶ Analog Filters

Chapter Ⅷ Distributions

Chapter Ⅹ Filters and Distributions

Chapter Ⅸ Convolution and the Fourier Transform of Distributions

Chapter Ⅺ Sampling and Discrete Filters

Chapter Ⅻ Current Trends: Time-Frequency Analysis

References

Index

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