Concept of Adaptive Filtering & Spline Adaptive Filtering Algorithm

A spline adaptive filter (SAF) based nonlinear active noise control (ANC) system is proposed in this paper. The SAF consists of a linear network of adaptive weights in a cascade with an adaptive nonlinear network. The nonlinear network in turn consists of an adaptive look-up table followed by a spline interpolation network and forms an adaptive activation function. An update rule has been derived for the proposed ANC system which not only updates the weights of the linear network but also updates the nature of the activation function. Linear Network is based on improvement in FxLMS algorithm. FxLMS algorithm is used because it is computationally simple like the most commonly used Least Mean Square (LMS) algorithm. In addition it includes secondary path effects. To make the FxLMS algorithm more effective the secondary path estimation should be more precise and accurate. The nonlinear function involved in the adaptation process is based on a spline function that can be modified during learning. The spline control points are adaptively changed using gradient-based techniques so B-splines and Catmull-Rom splines are used.