Just as a prism separates white light into its component bands of colored light, so the discrete Fourier transform (DFT) is used to separate a signal into its constituent frequencies. Just as a pair of sunglasses reduces the glare of white light, permitting only the softer green light to pass, so the DFT may be used to modify a signal to achieve a desired effect. In fact, by analyzing the component frequencies of a signal or any system, the DFT can be used in an astonishing variety of problems. Among the applications of the DFT are digital signal processing, oil and gas exploration, medical imaging, aircraft and spacecraft guidance, and the solution of differential equations of physics and engineering. The DFT: An Owner's Manual for the Discrete Fourier Transform explores both the practical and theoretical aspects of the DFT, one of the most widely used tools in science and engineering.
Author(s): William L. Briggs, Van Emden Henson
Publisher: Society for Industrial Mathematics
Year: 1987
Language: English
Pages: 453
The DFT: An Owner's Manual for the Discrete Fourier Transform......Page 3
ISBN 0-89871-342-0......Page 6
Contents......Page 9
Preface......Page 13
List of (Frequently and Consistently Used) Notation......Page 17
1 Introduction......Page 19
2 The Discrete Fourier Transform......Page 33
3 Properties of the DFT......Page 83
4 Symmetric DFTs......Page 135
5 Multidimensional DFTs......Page 161
6 Errors in the DFT......Page 197
7 A Few Applications of the DFT......Page 253
8 Related Transforms......Page 327
9 Quadrature and the DFT......Page 375
10 The Fast Fourier Transform......Page 397
Appendix: Table of DFTs......Page 419
Bibliography......Page 427
Index......Page 437
