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A New Twist to Fourier Transforms

A New Twist to Fourier Transforms

Hamish D. Meikle

ISBN: 978-3-527-40441-4

Feb 2004

238 pages

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Description

Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.
The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs.

1. The Fourier Transform and the Helix. 3. Fourier Transforms.

4. Continuous, Finite, and Discrete Fourier Transforms.

5. Tapering Functions.

6. Fourier Transforms in Statistics.

7. Noise and Pseudo-random Signals.

Appendix A: Glossary.

Appendix B: Maple Graphical Expressions.

Index.