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Fourier transforms : principles and applications /
"Fourier Analysis with Complex Variables explains transform methods and their application to electrical systems from circuits, antennas, and signal processors--ably guiding readers from vector space concepts to the Discrete Fourier Transform (DFT) and the Fourier series. Featuring chapter end s...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, New Jersey :
John Wiley & Sons,
[2014]
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| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
Tabla de Contenidos:
- 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 Approximation2.3 Infinite-dimensional vector spaces; 2.3.1 Convergent Sequences; 2.3.3 Functions and the Lp Spaces; 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 series4.4 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 Systems5.5.3 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 transform6.4.1 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; 6.7 Summary; Problems; 7 Complex Function Theory; 7.1 Complex functions and their visualization; 7.2 Differentiation; 7.3 Analytic functions; 7.4 exp z and functions derived from it; 7.5 log z and functions derived from it