Fourier Transforms Principles and Applications.

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Detalles Bibliográficos
Autor principal: Hansen, Eric W.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2014.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • FOURIER TRANSFORMS
  • Contents
  • Preface
  • Philosophy and Distinctives
  • Flow of the Book
  • Suggested Use
  • Acknowledgments
  • 1 Review of Prerequisite Mathematics
  • 1.1 Common notation
  • 1.2 Vectors in space
  • 1.3 Complex numbers
  • 1.4 Matrix algebra
  • 1.5 Mappings and functions
  • 1.6 Sinusoidal functions
  • 1.7 Complex exponentials
  • 1.8 Geometric series
  • 1.9 Results from calculus
  • 1.10 Top 10 ways to avoid errors in calculations
  • Problems
  • 2 Vector Spaces
  • 2.1 Signals and vector spaces
  • 2.2 Finite-dimensional vector spaces
  • 2.2.1 Norms and Metrics
  • 2.2.2 Inner Products
  • 2.2.3 Orthogonal Expansion and Approximation
  • 2.3 Infinite-dimensional vector spaces
  • 2.3.1 Convergent Sequences
  • 2.3.2 Infinite Sequences and the p Spaces
  • 2.3.3 Functions and the Lp Spaces
  • 2.3.4 Orthogonal Expansions in 2 and L2
  • 2.4 Operators
  • 2.5 Creating orthonormal bases-the Gram-Schmidt process
  • 2.6 Summary
  • Problems
  • 3 The Discrete Fourier Transform
  • 3.1 Sinusoidal sequences
  • 3.2 The Discrete Fourier transform
  • 3.3 Interpreting the DFT
  • 3.4 DFT properties and theorems
  • 3.5 Fast Fourier transform
  • 3.6 Discrete cosine transform
  • 3.7 Summary
  • Problems
  • 4 The Fourier Series
  • 4.1 Sinusoids and physical systems
  • 4.2 Definitions and interpretation
  • 4.3 Convergence of the Fourier series
  • 4.4 Fourier series properties and theorems
  • 4.5 The heat equation
  • 4.6 The vibrating string
  • 4.7 Antenna arrays
  • 4.8 Computing the Fourier series
  • 4.9 Discrete time Fourier transform
  • 4.9.1 Convergence Properties
  • 4.9.2 Theorems
  • 4.9.3 Discrete-time Systems
  • 4.9.4 Computing the DTFT
  • 4.10 Summary
  • Problems
  • 5 The Fourier Transform
  • 5.1 From Fourier series to Fourier transform
  • 5.2 Basic properties and some examples
  • 5.3 Fourier transform theorems
  • 5.4 Interpreting the Fourier transform
  • 5.5 Convolution
  • 5.5.1 Definition and basic properties
  • 5.5.2 Convolution and Linear Systems
  • 5.5.3 Correlation
  • 5.6 More about the Fourier transform
  • 5.6.1 Fourier inversion in L1
  • 5.6.2 Fourier Transform in L2
  • 5.6.3 More about convolution
  • 5.7 Time-bandwidth relationships
  • 5.8 Computing the Fourier transform
  • 5.9 Time-frequency transforms
  • 5.10 Summary
  • Problems
  • 6 Generalized Functions
  • 6.1 Impulsive signals and spectra
  • 6.2 The delta function in a nutshell
  • 6.3 Generalized functions
  • 6.3.1 Functions and Generalized Functions
  • 6.3.2 Generalized Functions as Sequences of Functions
  • 6.3.3 Calculus of Generalized Functions
  • 6.4 Generalized Fourier transform
  • 6.4.1 Definition
  • 6.4.2 Fourier Theorems
  • 6.5 Sampling theory and Fourier series
  • 6.5.1 Fourier Series, Again
  • 6.5.2 Periodic Generalized Functions
  • 6.5.3 The Sampling Theorem
  • 6.5.4 Discrete-time Fourier Transform
  • 6.6 Unifying the Fourier family
  • 6.6.1 Basis Functions and Orthogonality Relationships
  • 6.6.2 Sampling and Replication

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