Figure 10. Auto-MAC Color Plot of Tenth Order Pole Weighted Vectors, Above Threshold 4.7 Step 7: Identify and Retain Consistent Pole Weighted Vector Clusters Identify vector clusters from this pole weighted MAC diagram that represent the same pole weighted vector. This is done by taking the singular value decomposition (SVD) of the pole weighted MAC matrix. The number of significant singular values for this MAC matrix represents the number of significant pole clusters in the pole weighted vector matrix and the value of each significant singular value represents the size of the cluster since the vectors are unitary. Note that the singular value is nominally the square of the number of vectors in the cluster and will likely be different, mode by mode. Recognize also that Figure 10, as a thesholded Auto-MAC plot, will be largely zero and have significant magnitude (above the threshold) only for the pole weighted vectors that represent a cluster. 0 100 200 300 400 500 600 0 2 4 6 8 10 12 14 16 18 Cluster Number Weighted Pole Cluster Size Principal Value Cluster Figure 11. Principal Values of Clusters of Pole Weighted Vectors Figure 11 then is a plot of the scaled singular values for Figure 10. Each significant singular value as determined by a minimum cluster size threshold (typically 4) represents a cluster of pole weighted vectors with an equivalent spatio-temporal characteristic. The location of the corresponding pole weighted vectors in the pole weighted vector matrix (index) is found 374
RkJQdWJsaXNoZXIy MTMzNzEzMQ==