Frequency domain spline adaptive filters

Spline adaptive filter (SAF) is a kind of simple and effective nonlinear system online identification method. When the length of FIR filter, which represents the linear sub-model, is very long, the computational complexity will increase dramatically. In order to solve this problem, a frequency domain spline adaptive filter (FDSAF) is proposed in this paper. The filtering and adaptive processes in FIR filter are implemented in frequency domain, which transforms convolution in time domain into multiplication in frequency domain. In FDSAF, the fast Fourier transform (FFT) and its inverse transform (IFFT) are utilized, and the overlap-save method is adopted in order to improve the computational efficiency. In this paper, detailed procedures of FDSAF are derived. In addition, the bound on learning rate and computational complexity of the algorithm are analyzed. Finally, several numerical experiments are implemented in order to verify the effectiveness of FDSAF, and the results show that the proposed FDSAF can significantly reduce the computational complexity on the premise of ensuring the convergence performance compared with the traditional time domain SAF algorithm.