Figure 8
Block diagram of the overlapping waveform separation algorithm using template optimization in phase space (TOPS clustering algorithm, second step). (a) Real overlapping waveform. The arrows indicate the fundamental minima and the different points (from 1 to 7) are the zeros. (b) Raw segment profiles (dashed traces) extracted from the real overlapping waveform according to the criterion for the fundamental minima. Each segment in time domain corresponds to a quasi-closed trajectory in the phase space. (c) Single-unit templates (gray traces) obtained from K-means clustering (first step). Here are also indicated the extracted segments in time domain (black traces) corresponding to quasi-closed trajectories in the phase space. (d) Artificial overlapping waveform obtained by linear superposition of the single-unit templates with time shift sequences smaller than 2 ms between peaks. (e) Phase space portrait and the new variables θ (phase) and n(θ) (normal deviation) that were introduced to describe the trajectory of the analyzed signal (i.e., the reconstructed raw segment profile Si in the phase space, see dashed trace). The length of the vector |n(θ)| corresponds to the minimal distance between the signal Si and the limit trajectory Tj (i.e., one reconstructed single-unit template Tj in the phase space, see black trace). P0, M and N are reference points of the trajectories in the phase space. Finally, to find the artificial overlapping waveform which resembles the real overlapping waveform as good as possible, the cross-correlation is applied between them, for all the combinations.
