A fast inverse NUFFT algorithm for computational electromagnetics

The fast Fourier transform (FFT) technique is a powerful and practical numerical tool. The FFT algorithm requires the input data to be uniformly spaced. In some applications, however, the input data is not equally spaced. Thus, the nonuniform fast Fourier transform (NUFFT) algorithm is proposed for nonuniformly sampled data in the time-domain or frequency-domain with a computational complexity O(mN log₂N) (Liu, Q.H. and Tang, X.Y., Electronics Letters., vol.34, no.20, p.1913-14, 1998). The inverse NUFFT is realized by combining the conjugate gradients (CG) fast Fourier transform with the newly developed NUFFT algorithms. In these procedures, the CG-FFT is the most expensive with O(kN log₂N) arithmetic operations, where the number of iterations, k, in the CG algorithm is proportional to the conditioner number of Toeplitz matrix equations. The loose generalized minimal residual (LGMRES) (Chen, R.S. et al., Microwave and Optical Technology Letters, vol.39, no.4, p.261-7, 2003) and regular FFT techniques are combined with the NUFFT algorithms to develop an accurate NUIFFT algorithm. Our numerical results demonstrate that this method is much faster than CG-FFT in NUIFFT in terms of both the CPU time and convergence.