Spline Interpolation Based FFT Simulation Algorithm

Abstract

Spline interpolation based fast Fourier transform (FFT), referred to as the SFFT, is proposed in the present paper to further enhance the computational speed of simulating the multivariate stochastic processes. The SFFT algorithm is to mainly introduce the spline interpolation technique to reduce the number of the Cholesky decomposition of a spectral density matrix, as a result, further enhancing the simulation computational speed. In order to highlight the superiority of the SFFT algorithm, the simulations of the multivariate stationary longitudinal wind velocity fluctuations have been carried out, respectively, by resorting to the SFFT- and FFT-based spectral representation (SR) methods, in particular, taking into consideration that the elements of cross-power spectral density matrix are the complex values. The results show that the SFFT algorithm can achieve the results without a loss of precision with reference to the FFT algorithm. More importantly, the SFFT algorithm provides much higher computational efficiency. Likewise, the superiority of the SFFT algorithm is becoming more remarkable with the dividing number of frequency, the number of samples, and the time length of samples going up.