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Algorithm 2 Rearrangement for smooth decomposition.

Algorithm 2 describes a simple rearrangement procedure to track eigenvectors (singular vectors) for smooth decomposition.

Since the energy of highest order coefficients of eigenvectors are trifling, using the proposed method for smooth decomposition results in very high accuracy, as seem in the figures.

If at each frequency sample all singular values are in decreasing order, REARRANGE function (which is described in Algorithm 2) is only required for smooth decomposition, otherwise for spectral majorization, no further arrangement is required.

Figure 8 Eigenvalues of smooth decomposition versus frequency.

Relative error of smooth decomposition versus M is shown in Figure 11. Figure 11 Relative error of smooth decomposition versus M. While using frequency smooth EVD of (35) leads to relative error below 10−5 for M ≥ 3 with a few number of iterations, Spectrally majorized EVD requires a lot more polynomial order to reach a reasonable relative error.

A plot of E i versus iteration for M = 3 and smooth decomposition is depicted in Figure 10.

Therefore, a low order polynomial is required using smooth decomposition and much higher polynomial order for spectrally majorized decomposition.

Since eigenvalues intersect at two frequencies, smooth decomposition and spectrally majorized decomposition result two distinct solutions.

Since smooth decomposition leads to more compact decomposition, in cases that the only objective is strong decorrelation, exploiting smooth decomposition is reasonable.

Figure 10 E i versus iteration number corresponding to smooth decomposition.