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The Fourier Transform

  • Kenneth Lange
Chapter
Part of the Statistics and Computing book series (SCO)

Abstract

The Fourier transform is one of the most productive tools of the mathematical sciences. It crops up again and again in unexpected applications to fields as diverse as differential equations, numerical analysis, probability theory, number theory, quantum mechanics, optics, medical imaging, and signal processing [3, 5, 7, 8, 9]. One explanation for its wide utility is that it turns complex mathematical operations like differentiation and convolution into simple operations like multiplication. Readers most likely are familiar with the paradigm of transforming a mathematical equation, solving it in transform space, and then inverting the solution. Besides its operational advantages, the Fourier transform often has the illuminating physical interpretation of decomposing a temporal process into component processes with different frequencies.

Keywords

Fourier Transform Saddle Point Integrable Function Moment Generate Function Saddle Point Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer New York 2010

Authors and Affiliations

  1. 1.Departments of Biomathematics, Human Genetics, and Statistics David Geffen School of MedicineUniversity of California, Los AngelesLos AngelesUSA

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