A HIGH ACCURACY CONFORMAL METHOD FOR EVALUATING THE DISCONTINUOUS FOURIER TRANSFORM

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.