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An efficient method for the calculation of the interactions of a 2m factorial experiment was introduced by Yates and is widely known by his name. The generalization to 3m was given by Box et al. Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series. In their full generality, Good's methods are applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices, where m is proportional to log N. This results in a procedure requiring a number of operations proportional to N log N rather than N2. These methods are applied here to the calculation of complex Fourier series. They are useful in situations where the number of data points is, or can be chosen to be, a highly composite number. The algorithm is here derived and presented in a rather different form.


  • Autor/es: J.W. Cooley, J.W. Tukey.
  • Fecha: 1965-01
  • Publicado en: Mathematics of Comp., vol. 19, pp. 297-301, 1965.
  • Idioma: Inglés
  • Formato: PDF
  • Contribución: Aníbal Figueiras.
  • Palabras clave: Matemáticas, Proceso de señal

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