Abstract 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.

中文翻译：

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频域样条自适应滤波器

摘要 样条自适应滤波器(SAF)是一种简单有效的非线性系统在线辨识方法。当代表线性子模型的FIR滤波器的长度很长时，计算复杂度会急剧增加。为了解决这个问题，本文提出了一种频域样条自适应滤波器（FDSAF）。FIR滤波器中的滤波和自适应过程是在频域中实现的，将时域的卷积转化为频域的乘法。FDSAF利用快速傅里叶变换(FFT)及其逆变换(IFFT)，并采用重叠保存方法来提高计算效率。在本文中，推导出了FDSAF 的详细程序。此外，分析了算法的学习率和计算复杂度的界限。最后，通过几个数值实验验证了FDSAF的有效性，结果表明，与传统的时域SAF算法相比，所提出的FDSAF在保证收敛性能的前提下，可以显着降低计算复杂度。