Fourier transforms and convolutions for the experimentalist : R. C. Jennison. 1961. London: Pergamon Press Ltd. Pp. 120. £1 10s.
✍ Scribed by J.A. Hudson
- Publisher
- Elsevier Science
- Year
- 1962
- Tongue
- English
- Weight
- 216 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0013-4686
No coin nor oath required. For personal study only.
✦ Synopsis
IN HIS introduction, Dr. Jennison states his intention of demonstrating the use of the Fourier theorem as a tool, rather than of following its mathematical derivation. His book contains many examples of the use of the transform, drawn mainly from optics and aerial theory.
In the first chapter, the Fourier transform is described aa a method of writing a function of length or of time as a spectral function, the idea being illustrated when the reader is introduced to the delta function. The introduction to the subject is completed by examples of transforms of more complex distributions, such as rectangular and trigonometric functions.
Probably the most useful part of the book is chapter four, which consists of applications of transform theory to optical, aerial and acoustic problems, and ends with a list of methods of evaluation of transforms.
Chapter five contains an introduction to convolutions and a demonstration of their equivalence to the Fourier transform together with its inverse, again illustrated by examples. The use of the convolution theorem to evaluate transforms, however, seems to require greater mathematical intuition than is expected elsewhere in the book. The differentiation of transforms is discussed and also the use of the auto-correlation function. The book ends with an account of a few analogue machines which may be used to compute transforms numerically, and tables of three functions which commonly arise in the use of Fourier transforms.
The experimental scientist, to whom the book is addressed, will probably find the author's examples and frequent use of diagrams most helpful. However, the style of writing makes the book rather difficult to follow, particularly in the first two chapters, and the introduction of the reader to the delta function transform is a somewhat abrupt beginning to the study of the subject. The justification of the use of negative frequencies seems unnecessary, since the Fourier integral may be used in a form which includes only positive and zero frequencies. Negative frequencies are included as a matter of convenience and elegance. The complex rather than the real form of the integral is used for the same reason. . The later chapters of the book should serve very well as a 'guide to the. . . practical use of the Fourier transform'. J. A. HUDSON