A Low Computational Complexity Family of Spline NLMS Adaptive Filter Algorithm

This paper presents novel and low computational complexity spline adaptive filtering (SAF) algorithms based on partial coefficients selection and adaption. They are addressed partial update SAF normalized least mean squares (PU-SAF-NLMS) algorithms. The PU-SAF-NLMS equations are established via the steepest gradient descent constraint to the proposed cost function. In the proposed algorithms, the filter coefficients are updated based on periodic, sequential, and selective rules, leading to reduction in computational complexity. Furthermore, the convergence speed of PU-SAF-NLMS algorithms is close to the conventional SAF-NLMS. Moreover, the convergence analysis of algorithms is studied. Ultimately, the performance of the presented algorithms is appraised through several experimental results.