Concept of Adaptive Filtering

Shivendra Nandan

Theory Books Book 3 · TSG Publications

About this eBook

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. B-splines and Catmull-Rom splines are used, because they allow imposing simple constraints on control parameters. This new kind of adaptive function is then applied to the output of a linear adaptive filter and it is used for the identification of Wiener-type nonlinear systems. In addition, we derive a simple form of the adaptation algorithm and an upper bound on the choice of the step-size. An extensive simulation study has been conducted to evaluate the noise mitigation performance of the proposed scheme and the new method has been shown to provide improved noise cancellation efficiency with a lesser computational load in comparison with other popular ANC systems.

 

About the author

Shivendra Nandan is the former State Representative (Technical Education) of the Government of Rajasthan. He provided eminent support in the implementation of the National Education Policy in Technical Education. Being a Chartered Engineer and Gold Medalist in his Bachelor, his Ideas were selected for review in the Idea and Innovation exhibition organized by the Council of Science and Technology UP and Got the prize.

He is a member of prestigious engineering societies such as the International Association of Engineers, Institution of Engineers (India), ASME, and ASHRAE. In the field of research, he begins with articles in different domains such as Thermal, Renewable energy, and Design Aspects. Later on, he constrained himself in the field of soft materials and computational mechanics. Later on, he became a reviewer of more than 10 prestigious journals and editor of "Futuristics Trends in Mechanical Engineering Journal".

He is the Host and Anchor of "Talk Show on Mechanical Engineering", which is declared as one of the Top 20 Podcasts on Mechanical Engineering in 2021 by Welp magazine. Further, he is serving as Design Engineer in Mercedes-Benz Research & Development India (MBRDI), Pune.