Efficient Implementation of The Second Order Volterra Filter

Abstract – This paper investigates a new implementation of the second order isotropic filter using the Walsh Hadamard Transform. The new implementation is used in a second order Volterra filter. It’s performances are evaluated in a typical nonlinear system identification application. For the second order adaptive Volterra filter an LMS adaptive algorithm with variable step size for the linear and the quadratic parts is proposed. Experimental results show that by using the WHT, the computational complexity of the adaptive second order filter is considerably reduced and the convergence rate of this filter is also significantly improved. Adaption is working well even for high levels of the input signal. The mean-squared error of the proposed filter is compared with those of a classic second order LMS adaptive filter