Life in the fast lane

Yates’s algorithm, fast fourier and walsh transforms

Paul J. Sanchez, John S. Ramberg, Kenneth L Head

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Orthogonal functions play an important role in factorial experiments and time series models. In the latter half of the twentieth century orthogonal functions became prominent in industrial experimentation methodologies that employ complete and fractional factorial experiment designs, such as Taguchi orthogonal arrays. Exact estimates of the parameters of linear model representations can be computed effectively and efficiently using “fast algorithms.” The origin of “fast algorithms” can be traced to Yates in 1937. In 1958 Good created the ingenious fast Fourier transform, using Yates’s concept as a basis. This paper is intended to illustrate the fundamental role of orthogonal functions in modeling, and the close relationship between two of the most significant of the fast algorithms. This in turn yields insights into the fundamental aspects of experiment design.

Original languageEnglish (US)
Title of host publicationInternational Series in Operations Research and Management Science
PublisherSpringer New York LLC
Pages651-684
Number of pages34
Volume46
StatePublished - 2016
Externally publishedYes

Publication series

NameInternational Series in Operations Research and Management Science
Volume46
ISSN (Print)08848289

Fingerprint

Walsh Transform
Walsh transforms
Orthogonal functions
Orthogonal Functions
Fast Fourier transform
Fast Fourier transforms
Fast Algorithm
Factorial Experiment
Fractional Factorial
Orthogonal Array
Design of Experiments
Time Series Models
Design of experiments
Experimentation
Time series
Linear Model
Experiments
Methodology
Modeling
Estimate

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Strategy and Management
  • Applied Mathematics
  • Computer Science Applications
  • Software

Cite this

Sanchez, P. J., Ramberg, J. S., & Head, K. L. (2016). Life in the fast lane: Yates’s algorithm, fast fourier and walsh transforms. In International Series in Operations Research and Management Science (Vol. 46, pp. 651-684). (International Series in Operations Research and Management Science; Vol. 46). Springer New York LLC.

Life in the fast lane : Yates’s algorithm, fast fourier and walsh transforms. / Sanchez, Paul J.; Ramberg, John S.; Head, Kenneth L.

International Series in Operations Research and Management Science. Vol. 46 Springer New York LLC, 2016. p. 651-684 (International Series in Operations Research and Management Science; Vol. 46).

Research output: Chapter in Book/Report/Conference proceedingChapter

Sanchez, PJ, Ramberg, JS & Head, KL 2016, Life in the fast lane: Yates’s algorithm, fast fourier and walsh transforms. in International Series in Operations Research and Management Science. vol. 46, International Series in Operations Research and Management Science, vol. 46, Springer New York LLC, pp. 651-684.
Sanchez PJ, Ramberg JS, Head KL. Life in the fast lane: Yates’s algorithm, fast fourier and walsh transforms. In International Series in Operations Research and Management Science. Vol. 46. Springer New York LLC. 2016. p. 651-684. (International Series in Operations Research and Management Science).
Sanchez, Paul J. ; Ramberg, John S. ; Head, Kenneth L. / Life in the fast lane : Yates’s algorithm, fast fourier and walsh transforms. International Series in Operations Research and Management Science. Vol. 46 Springer New York LLC, 2016. pp. 651-684 (International Series in Operations Research and Management Science).
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