A delta-method technique in the wavelet domain to determine statistical quantities of the response of electromagnetic devices with uncertain parameters

In this paper a method to determine the mean value and the variance of the response of a system with uncertain parameters is proposed. With the term 'response of a system' we indicate either the value of a single parameter that represents a figure of merit of a device (e.g. the efficiency of a transmission system or the band width of a communication channel) or a characteristic function of the system (e.g. the impulse or the frequency response). In the latter case we estimate the mean value and the variance at every sample of the response. The estimate is performed by using the delta method, a technique for approximating expected values of functions of random variables when the direct evaluation is not feasible. Two examples of the application of the proposed procedure are reported and the results are compared with simulations performed by a Monte Carlo analysis.