The paper describes a higher-order statistics (HOS) approach feasible for decomposition of compound signals. It shows how important is to take into account the complete cumulant-induced information, like it is done by bicepstral system identification. Even this one fails with highly superimposed signals, like surface electromyograms (SEMGs), mainly owing to cepstral aliasing. Our novel method introduces asymptotically exact interpolation-based computation of bicepstra with no aliasing. We analysed it in order to establish the conditions under which SEMGs could be decomposed onto their building components, i.e. motor-unit action potentials. The experiments with synthetic SEMGs showed that the results depend highly on the type of the action potentials (APs) respected. Using our novel bicepstral decomposition, the first-norm error for the dipole-based APs falls under 50 % of the mean absolute value of the signal samples only with the signals of lengths of over 110000 samples and interpolation level of 4096. The situation with tripole-generated APs is easier, giving errors below 50 % already at signal lengths of 10000 and interpolation level of 4096. Nevertheless, both mean the EMG recordings of duration under 30 s, which assures stationary conditions at moderate contraction forces. The developed decomposition approach can, therefore, be considered suitable for further HOS-based decomposition of SEMGs.