TY - GEN

T1 - A note on relation between the Fourier coefficients and the effects in the experimental design

AU - Ukita, Yoshifumi

AU - Matsushima, Toshiyasu

PY - 2011/12/1

Y1 - 2011/12/1

N2 - It has recently been shown that the model in experimental design can be expressed in terms of an orthonormal system. In this case, the model is expressed by using Fourier coefficients instead of the effect of each factor. As there is an abundance of software for calculating the Fourier transform, such a system allows for a straightforward implementation of the procedures for estimating the Fourier coefficients by using Fourier transform. However, Fourier coefficients themselves do not provide a direct representation of the effect of each factor, and the relation between the Fourier coefficients and the effect of each factor has not yet been clarified. In this paper, we present theorems of the relation between the Fourier coefficients and the effect of each factor. By using these theorems, the effect of each factor can be easily obtained from the computed Fourier coefficients. Therefore, with the aid of an orthonormal system, it is possible to easily implement the estimation procedures as well as to understand how each factor affects the response variable in the model.

AB - It has recently been shown that the model in experimental design can be expressed in terms of an orthonormal system. In this case, the model is expressed by using Fourier coefficients instead of the effect of each factor. As there is an abundance of software for calculating the Fourier transform, such a system allows for a straightforward implementation of the procedures for estimating the Fourier coefficients by using Fourier transform. However, Fourier coefficients themselves do not provide a direct representation of the effect of each factor, and the relation between the Fourier coefficients and the effect of each factor has not yet been clarified. In this paper, we present theorems of the relation between the Fourier coefficients and the effect of each factor. By using these theorems, the effect of each factor can be easily obtained from the computed Fourier coefficients. Therefore, with the aid of an orthonormal system, it is possible to easily implement the estimation procedures as well as to understand how each factor affects the response variable in the model.

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U2 - 10.1109/ICICS.2011.6173126

DO - 10.1109/ICICS.2011.6173126

M3 - Conference contribution

AN - SCOPUS:84860633140

SN - 9781457700309

T3 - ICICS 2011 - 8th International Conference on Information, Communications and Signal Processing

BT - ICICS 2011 - 8th International Conference on Information, Communications and Signal Processing

T2 - 8th International Conference on Information, Communications and Signal Processing, ICICS 2011

Y2 - 13 December 2011 through 16 December 2011

ER -