On the usage of Dirac Delta functions with nonlinear argument in high order I/O integrals

The effect of using a Dirac Delta function with polynomial argument in mathematical methodologies based on nonlinear I/O integrals, is studied. In concrete, we present the case where a Dirac Delta function plays the role of input or transfer function which would turn out to be of importance to model nonlinear systems containing distortion or degradation in their output signals. In effect, is seen the presence of sub-harmonics as consequence of quadratic argument into the Dirac Delta function when it enters into an I/O convolution integral. This mathematical methodology presents clearly some virtues which might be employed to the case where a fully disturbed simulated signal can be modeled with 6 parameters identification curve based on the Dirac Delta functions with polynomial argument. The discrepancy between simulated data and model yields an error of order of up to 8%. In other case, is required up to 9 parameters when the formalism is adjusted to model path-loss signal in wireless communications, with an error of order of 5%, thereby indicating that the modeling with Dirac Delta functions might be advantageous to model nonlinear systems variables plagued of stochastic disturbs.