### Abstract

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.

Original language | English |
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Title of host publication | ICICS 2011 - 8th International Conference on Information, Communications and Signal Processing |

DOIs | |

Publication status | Published - 2011 |

Event | 8th International Conference on Information, Communications and Signal Processing, ICICS 2011 - Singapore Duration: 2011 Dec 13 → 2011 Dec 16 |

### Other

Other | 8th International Conference on Information, Communications and Signal Processing, ICICS 2011 |
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City | Singapore |

Period | 11/12/13 → 11/12/16 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Networks and Communications
- Information Systems
- Signal Processing

### Cite this

*ICICS 2011 - 8th International Conference on Information, Communications and Signal Processing*[6173126] https://doi.org/10.1109/ICICS.2011.6173126

**A note on relation between the Fourier coefficients and the effects in the experimental design.** / Ukita, Yoshifumi; Matsushima, Toshiyasu.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ICICS 2011 - 8th International Conference on Information, Communications and Signal Processing.*, 6173126, 8th International Conference on Information, Communications and Signal Processing, ICICS 2011, Singapore, 11/12/13. https://doi.org/10.1109/ICICS.2011.6173126

}

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

Y1 - 2011

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.

UR - http://www.scopus.com/inward/record.url?scp=84860633140&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860633140&partnerID=8YFLogxK

U2 - 10.1109/ICICS.2011.6173126

DO - 10.1109/ICICS.2011.6173126

M3 - Conference contribution

SN - 9781457700309

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

ER -