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PIER PIER B PIER C PIER M PIER Letters
2010-11-06
A High Accuracy Conformal Method for Evaluating the Discontinuous Fourier Transform
By
Chun-Hui Zhu,

    Dr. Chun-Hui Zhu

    Department of Control Science and Engineering

    Harbin Institute of Technology

    China

    Homepage

Qing Huo Liu,

    Prof. Qing Huo Liu

    Department of Electrical and Computer Engineering

    Duke University

    USA

    Homepage

Yi Shen,

    Dr. Yi Shen

    Department of Control Science and Engineering

    Harbin Institute of Technology

    China

    Homepage

Lijun Liu

    Dr. Lijun Liu

    Department of Control Science and Engineering

    Harbin Institute of Technology

    China

    Homepage

Progress In Electromagnetics Research, Vol. 109, 425-440, 2010
doi:10.2528/PIER10082007
Abstract
A highly accurate, fast algorithm is proposed to evaluate the finite Fourier transform of both continuous and discontinues functions. As the discretization is conformal to the function discontinuities, this method is called the conformal Fourier transform (CFT) method. It is applied to computational electromagnetics to calculate the Fourier transform of induced electric current densities in a volume integral equation. The spectral discrimination in the CFT method can be arbitrary and the spectral range can be as large as needed. As no discretization for the Fourier exponential kernel is needed, the CFT method is not restricted by the Nyquist sampling theorem, thus avoiding the aliasing distortions that exist in other traditional methods. The accuracy of the CFT method is greatly improved since the method is based on high order interpolation and the closed-form Fourier transforms for polynomials partly reduce the error due to discretization. Assuming Ns and N are the numbers of sampling points in the spatial and frequency domain, respectively, the computational cost of the CFT method is O((M + 1)N log2L), where M is the interpolation order and L=(Ns−1)/M. Applications in spectral analysis of electromagnetic fields are demonstrated.
Citation
Chun-Hui Zhu, Qing Huo Liu, Yi Shen, and Lijun Liu, "A High Accuracy Conformal Method for Evaluating the Discontinuous Fourier Transform," Progress In Electromagnetics Research, Vol. 109, 425-440, 2010.
doi:10.2528/PIER10082007
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