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

Yoshifumi Ukita, Toshiyasu Matsushima

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    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 languageEnglish
    Title of host publicationICICS 2011 - 8th International Conference on Information, Communications and Signal Processing
    DOIs
    Publication statusPublished - 2011
    Event8th International Conference on Information, Communications and Signal Processing, ICICS 2011 - Singapore
    Duration: 2011 Dec 132011 Dec 16

    Other

    Other8th International Conference on Information, Communications and Signal Processing, ICICS 2011
    CitySingapore
    Period11/12/1311/12/16

    Fingerprint

    Design of experiments
    Fourier transforms

    ASJC Scopus subject areas

    • Computer Networks and Communications
    • Information Systems
    • Signal Processing

    Cite this

    Ukita, Y., & Matsushima, T. (2011). A note on relation between the Fourier coefficients and the effects in the experimental design. In 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.

    ICICS 2011 - 8th International Conference on Information, Communications and Signal Processing. 2011. 6173126.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Ukita, Y & Matsushima, T 2011, A note on relation between the Fourier coefficients and the effects in the experimental design. in 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
    Ukita Y, Matsushima T. A note on relation between the Fourier coefficients and the effects in the experimental design. In ICICS 2011 - 8th International Conference on Information, Communications and Signal Processing. 2011. 6173126 https://doi.org/10.1109/ICICS.2011.6173126
    Ukita, Yoshifumi ; Matsushima, Toshiyasu. / A note on relation between the Fourier coefficients and the effects in the experimental design. ICICS 2011 - 8th International Conference on Information, Communications and Signal Processing. 2011.
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