Nonlinear convolution and fourier series coefficients estimate

In the present the paper an original description of the procedure for the modeling of nonlinear systems based on the socalled non linear convolution approach [1, 2, 3] is reported. This approach relies on the modeling of a nonlinear system by means of the linear convolution and we show how, in the case of memoryless nonlinear systems, the method is related to the Fourier Series representation of nonlinear system's output. Based on these observations a Fourier Series implementation of the model is proposed, which allows a significant reduction in the associated computational cost. Experimental results confirm the validity of the proposed Fourier Series implementation of the nonlinear convolution based modeling technique.