Identifiability of the superimposed signals using third-order cumulants

Abstract

The paper deals with the variance analysis estimating the third-order cumulant of the MA system output signal which was excited with Bernoulli distributed white noise on the input. These scheme was used to simulate the superimposed systems, or signals, which often arise in the practical approaches (EMG signal decomposition). The equations were derived which show dependencies of the variances of the third-order output cumulant values on the length of the output signal and on the values of the samples in the impulse response of the unknown system as well. The structure of the variance inside the third-order cumulant array was observed. The speed and the convergence of the identification procedure could be predicted using these results for the case of superimposed MA systems. The knowledge of the structure of the variance is helpful in designing new identification methods. Some examples are given to show the correctness of the derived equations.