Normalized Subband Spline Adaptive Filter: Algorithm Derivation and Analysis
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Normalized Subband Spline Adaptive Filter: Algorithm Derivation and Analysis Pengwei Wen1 · Jiashu Zhang2 · Sheng Zhang2 · Boyang Qu1 Received: 10 February 2020 / Revised: 14 October 2020 / Accepted: 17 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper proposes a normalized subband spline adaptive filter (SAF-NSAF) algorithm to solve the problem that linear subband adaptive filtering cannot identify nonlinear systems. The weight update of the proposed algorithm is conducted using the principle of minimum disturbance. Since a delayless structure is used in the proposed algorithm, a delay is not introduced into the update process. The effectiveness of the proposed algorithm is verified by simulations. Also, the mean and mean square stability of the proposed algorithm are evaluated using the principle of conservation of energy. The simulation results demonstrate that the performance of the proposed algorithm outperforms other cited nonlinear algorithms. Keywords Spline adaptive filter · Delayless subband adaptive filter · Nonlinear adaptive filter
1 Introduction Subband adaptive filters have been widely used in many practical applications because of their simple design and easy implementation [20, 27]. Benefiting from the structural
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Pengwei Wen [email protected] Boyang Qu [email protected] Jiashu Zhang [email protected] Sheng Zhang [email protected]
1
School of Electronic and Information Engineering, Zhongyuan University of Technology, Zhengzhou 450007, Henan, China
2
School of Information Science and Technology, Southwest Jiaotong University, Chengdu 611756, China
Circuits, Systems, and Signal Processing
advantages, namely, the full-band input signal can be decomposed into almost mutually repulsive subband signals using the analysis filter bank and subsampling, and these subband signals are then recombined into a full-band signal through synthetic filter banks, the subband adaptive filters can increase the algorithm convergence speed in the case of the input covariance matrix with a large eigenvalue spread, such as highly correlated speech input signals [11–13, 28]. Many subband adaptive filtering algorithms have been proposed for identifying unknown linear systems, including the conventional normalized subband adaptive filter (NSAF) algorithm [13], sign subband adaptive filter (SSAF) algorithm [17], delayless normalized subband adaptive filter (DNSAF) algorithm [10, 15, 16], variable step-size NSAF algorithm [7, 18, 29, 30], variable step-size SSAF algorithm [8, 31], and many others [19]. A more detailed description of the linear subband adaptive filters can be found in [12]. Although the subband adaptive filtering algorithms for linear systems are very mature, the design of subband adaptive filtering algorithms for nonlinear systems is still in the developing stage. A few subband adaptive filtering algorithms for nonlinear systems have been proposed. Based on the Volterra structure, a subband Volterra structure was proposed, which
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