Algorithm 4 Estimating scales from data using Hankel DMD

Input: time step: $\Delta x$, time series f: $f\left[n\right]=f(\Delta xn)$, length of time series vector: N, tolerance for support: $tol$, $\eta$, M: number of rows of Hankel matrix 1: H = Hankel matrix made from f with M rows and N-M columns 2: $rez,\lambda ,Vtn=DMD\_RRR\left(H\right)$ 3: $\omega =\frac{1}{2\pi i}ln\left(\frac{\lambda }{\left|\lambda \right|}\right)$ 4: $T=0$ 5: for i = 0 to N − 1: 6:    $E\left[i\right]=|\langle Y[:,0],Vtn[:,i]\rangle |$ 7:    $T=T+E{\left[i\right]}^2$ 8: $T=\sqrt{T}$ 9: $S_{DMD}=\left[\right]$ 10: for i = 0 to N − 1: 11:    if $rez\left[i\right]<tol$ and $energy\left[i\right]>\eta T$ 12:       $S_{DMD}.append\left(\omega \left[i\right]\right)$ 13: return ${\sigma }_{DMD}=\frac{\Delta x}{6S_{DMD}}$