Fourier series and transforms
Bracewell, Ronald N. Formerly, Electrical Engineering Department, Stanford University, Stanford, California.
- Fourier series
- Fourier transforms
- Discrete Fourier transform
- Hartley transform
- Fast Fourier transform
- Additional Readings
Mathematical tools for the analysis of functions through decomposition into sinusoids. In 1822, J. Fourier proposed that ordinary mathematical functions could be represented by a sum of sinusoids, even though at first sight it might seem that the blandness and repetitive nature of the sinusoid ill suited it to accommodate the variety of functions in general. The advantage of such a representation is this: A differential equation that is difficult to solve under the untidy given external conditions that often arise in technology may very well be soluble under an external condition that is simply sinusoidal. If solutions can be obtained for each of the constituent sinusoids that make up the given external function, then perhaps the required solution will be the sum of the separate simple solutions. This was indeed so in the case studied by Fourier, who was interested in the differential equation governing the diffusion of heat in homogeneous solids; in fact, it is often the case that solving for sinusoids permits synthesis of the required solution. When this does happen, the solution is itself composed of sinusoids and there is said to be a sinusoidal response to sinusoidal input; the differential equation will also exhibit linearity combined with shift invariance. See also: Differential equation; Linearity; Spectrum analyzer; Trigonometry
The content above is only an excerpt.
for your institution. Subscribe
To learn more about subscribing to AccessScience, or to request a no-risk trial of this award-winning scientific reference for your institution, fill in your information and a member of our Sales Team will contact you as soon as possible.
to your librarian. Recommend
Let your librarian know about the award-winning gateway to the most trustworthy and accurate scientific information.
AccessScience provides the most accurate and trustworthy scientific information available.
Recognized as an award-winning gateway to scientific knowledge, AccessScience is an amazing online resource that contains high-quality reference material written specifically for students. Contributors include more than 9000 highly qualified scientists and 43 Nobel Prize winners.
MORE THAN 8500 articles and Research Reviews covering all major scientific disciplines and encompassing the McGraw-Hill Encyclopedia of Science & Technology and McGraw-Hill Yearbook of Science & Technology
115,000-PLUS definitions from the McGraw-Hill Dictionary of Scientific and Technical Terms
3000 biographies of notable scientific figures
MORE THAN 19,000 downloadable images and animations illustrating key topics
ENGAGING VIDEOS highlighting the life and work of award-winning scientists
SUGGESTIONS FOR FURTHER STUDY and additional readings to guide students to deeper understanding and research
LINKS TO CITABLE LITERATURE help students expand their knowledge using primary sources of information