Second Order Volterra-LMS Filter

Nonlinear System Identification using Second-Order Adaptive Volterra Filters: A #Generic Code

In this code, we will identify a nonlinear system using the traditional second-order adaptive Volterra filter. These type of filters are also known as linear-in-the-parameters nonlinear adaptive filters. The second-order Volterra expansion can be obtained from Table-I of this very recent paper:

X. Guo, Y. Li, J. Jiang, C. Dong, S. Du, and L. Tan, "Sparse Modeling of Nonlinear Secondary Path for Nonlinear Active Noise Control," in IEEE Transactions on Instrumentation and Measurement, vol. 67, no. 3, pp. 482-496, March 2018.

By the way, Prof. Li tan and Prof. J. Jiang are the "Inventors" of the Adaptive Volterra filter.

In this example, we have used this filter in a nonlinear system identification scenario, where the nonlinearity is introduced by the loudspeaker. For more details, please refer to the following paper from our lab.

V. Patel, V. Gandhi, S. Heda, and N. V. George, “Design of Adaptive Exponential Functional Link Network-Based Nonlinear Filters,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 63, no. 9, pp. 1434–1442, 2016.

In this code, example 1 (Case I of page 5) of the above paper with exact values of parameters is implemented.

The code is nicely scripted. Hope this helps!!!!!