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The Fourier Transform

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Book cover Numerical Analysis for Statisticians

Part of the book series: Statistics and Computing ((SCO))

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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.

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References

  1. Barndorff-Nielsen OE, Cox DR (1989) Asymptotic Techniques for Use in Statistics. Chapman and Hall, London

    MATH  Google Scholar 

  2. Daniels HE (1982) The saddlepoint approximation for a general birth process. J Appl Prob 19:20-28

    Article  MathSciNet  MATH  Google Scholar 

  3. Dym H, McKean HP (1972) Fourier Series and Integrals. Academic Press, New York

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  4. Feller W (1971) An Introduction to Probability Theory and Its Applications, Volume 2, 2nd ed. Wiley, New York

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  5. Folland GB (1992) Fourier Analysis and its Applications. Wadsworth and Brooks/Cole, Pacific Grove, CA

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  6. Hall P (1992) The Bootstrap and Edgeworth Expansion. Springer, New York

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  7. Körner TW (1988) Fourier Analysis. Cambridge University Press, Cambridge

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  8. Lighthill MJ (1958) An Introduction to Fourier Analysis and Generalized Functions. Cambridge University Press, Cambridge

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  9. Rudin W (1973) Functional Analysis. McGraw-Hill, New York

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Authors and Affiliations

  1. Departments of Biomathematics, Human Genetics, and Statistics David Geffen School of Medicine, University of California, Los Angeles, Le Conte Ave. 10833, Los Angeles, CA, 90095-1766, USA

    Kenneth Lange

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  1. Kenneth Lange
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Correspondence to Kenneth Lange .

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© 2010 Springer New York

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Lange, K. (2010). The Fourier Transform. In: Numerical Analysis for Statisticians. Statistics and Computing. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5945-4_19

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