6 Decomposition into independent modes

Figure 9: Component loadings of the principal components PC1 & PC2 for the ampligram of Fig. 8. X-axis shows variable/wavelet coefficient magnitude in 1% steps of 20% of its maximum value

The principal component analysis of the ampligram matrix must be performed to identify the number of significant independent components in the data. As a result the matrix of component loadings, being the correlation coefficients between significant principal components of the ampligram and the L rows of the ampligram, is obtained. An example of component loadings is shown in Fig. 9. The diagram shows which ranges of coefficient magnitude between 0 an 20% contribute to the two modes present in the data of Fig. 8. The mode 1 (dominating) corresponds to coefficient magnitudes 4-10% and the mode 2 corresponds to magnitudes of 1-4%. The non-linear filtering is now repeated once for each observed mode, the bandpass of magnitude is now selected from Fig. 9. The result, after the inverse wavelet transform, shows time series corresponding to the significant modes. An example of decomposed modes is shown in Fig. 10.

Figure 10: Modes decomposed from the signal of Fig. 8