Fourier Transforms: An Introduction for Engineers: 322 (The Springer International Series in Engineering and Computer Science, 322) - Hardcover

Gray, Robert M.; Goodman, Joseph W.

Hardcover

ISBN 10: 0792395859 ISBN 13: 9780792395850

Publisher: Springer, 1995

Synopsis

The Fourier transform is one of the most important mathematical tools in a wide variety of fields in science and engineering. In the abstract it can be viewed as the transformation of a signal in one domain (typically time or space) into another domain, the frequency domain. Applications of Fourier transforms, often called Fourier analysis or harmonic analysis, provide useful decompositions of signals into fundamental or "primitive" components, provide shortcuts to the computation of complicated sums and integrals, and often reveal hidden structure in data. Fourier analysis lies at the base of many theories of science and plays a fundamental role in practical engineering design. The origins of Fourier analysis in science can be found in Ptolemy's decomposing celestial orbits into cycles and epicycles and Pythagorus' de­ composing music into consonances. Its modern history began with the eighteenth century work of Bernoulli, Euler, and Gauss on what later came to be known as Fourier series. J. Fourier in his 1822 Theorie analytique de la Chaleur [16] (still available as a Dover reprint) was the first to claim that arbitrary periodic functions could be expanded in a trigonometric (later called a Fourier) series, a claim that was eventually shown to be incorrect, although not too far from the truth. It is an amusing historical sidelight that this work won a prize from the French Academy, in spite of serious concerns expressed by the judges (Laplace, Lagrange, and Legendre) re­ garding Fourier's lack of rigor.

About this title

Synopsis

The Fourier transform is one of the most important mathematical tools in a wide variety of science and engineering fields. Its application - as Fourier analysis or harmonic analysis - provides useful decompositions of signals into fundamental ('primitive') components, giving shortcuts in the computation of complicated sums and integrals, and often revealing hidden structure in the data. "Fourier Transforms: An Introduction for Engineers" develops the basic definitions, properties and applications of Fourier analysis, the emphasis being on techniques for its application to linear systems, although other applications are also considered. The book will serve as both a reference text and a teaching text for a one-quarter or one-semester course covering the application of Fourier analysis to a wide variety of signals, including discrete time (or parameter), continuous time (or parameter), finite duration, and infinite duration.It highlights the common aspects in all cases considered, thereby building an intuition from simple examples that will be useful in the more complicated examples where careful proofs are not included.

"Fourier Analysis: An Introduction for Engineers" is written by two scholars who are recognized throughout the world as leaders in this area, and provides a fresh look at one of the most important mathematical and directly applicable concepts in nearly all fields of science and engineering. This book is suitable for engineers, especially electrical engineers. The careful treatment of the fundamental mathematical ideas makes the book suitable in all areas where Fourier analysis finds applications.

Edition details

• Publisher: Springer
• Publication date: 1995
• Language: English
• ISBN 10: 0792395859
• ISBN 13: 9780792395850
• Binding: Hardcover
• Number of pages: 381