The DFT: An Owners' Manual for the Discrete Fourier Transform

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· 제목 : The DFT: An Owners' Manual for the Discrete Fourier Transform (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 미적분학
· ISBN : 9780898713428
· 쪽수 : 450쪽
· 출판일 : 1987-01-01

Preface
List of Frequently Used Terms
Chapter 1: Introduction. A Bit of History
An Application
Problems
Chapter 2: The Discrete Fourier Transform . Introduction
DFT Approximation to the Fourier Transform
The DFT-IDFT Pair
DFT Approximations to Fourier Series Coefficients
The DFT from Trigonometric Approximation
Transforming a Spike Train
Limiting Forms of the DFT-IDFT Pair
Problems
Chapter 3: Properties of the DFT. Alternate Forms for the DFT
Basic Properties of the DFT
Other Properties of the DFT
A Few Practical Considerations
Analytical DFTs
Problems
Chapter 4: Symmetric DFTs. Introduction
Real Sequences and the Real DFT (RDFT)
Even Sequences and the Discrete Cosine Transform (DST)
Odd Sequences and the Discrete Sine Transform (DST)
Computing Symmetric DFTs
Notes
Problems
Chapter 5: Multidimensional DFTs. Introduction
Two-Dimensional DFTs
Geometry of Two-Dimensional Modes
Computing Multi-Dimensional DFTs
Symmetric DFTs in Two Dimensions
Problems
Chapter 6: Errors in the DFT
Introduction
Periodic, Band-Limited Input
Periodic, Non-Band-Limited Input
Replication and the Poisson Summation Formula
Input with Compact Support
General Band-Limited Functions
General Input
Errors in the Inverse DFT
DFT Interpolation - Mean Square Error
Notes and References
Problems
Chapter 7: A Few Applications of the DFT. Difference Equations - Boundary Value Problems
Digital Filtering of Signals
FK Migration of Seismic Data
Image Reconstruction from Projections
Problems
Chapter 8: Related Transforms. Introduction
The Laplace Transform
The z-Transform
The Chebyshev Transform
Orthogonal Polynomial Transforms
The Discrete Hartley Transform (DHT)
Problems
Chapter 9: Quadrature and the DFT. Introduction
The DFT and the Trapezoid Rule
Higher Order Quadrature Rules
Problems
Chapter 10: The Fast Fourier Transform. Introduction
Splitting Methods
Index Expansions (One ---> Multi-dimensional)
Matrix Factorizations
Prime Factor and Convolution Methods
FFT Performance
Notes
Problems
Appendix: Table of Discrete Fourier Transforms
Bibliography.