Figure 1
From: Enhancing spectral analysis in nonlinear dynamics with pseudoeigenfunctions from continuous spectra
Left: Synthetic signal with aperiodicity; the data is an observed signal synthesized from signal 1 and signal 2 (\(x_1 (t)\) and \(x_2 (t)\) in Eq. (6)), which are harmonic oscillations with different frequencies and thermal noise. Middle: Pseudospectra (contours) and DMD eigenvalues (red dots) computed from the synthetic signal. The darker color indicates the common logarithm of the residuals computed by ResDMD. The darker the color, the smaller the residuals, indicating a distribution of DMD eigenvalues. Some spurious eigenvalues have large residuals. Right: Spectrum of DMD. The horizontal axis shows the argument of the complex (\(\lambda = e^{i \theta }\)) eigenvalues and the vertical axis shows the absolute values of the DMD coefficients. The two frequencies \(\omega _1\) and \(\omega _2\) in Eq. (6) are depicted as cyan vertical lines.
