Algorithm 1. Optimization Concept for VMD [14].
initialization $\left\{{\widehat{u}}_k^1\right\}, \left\{{\widehat{\omega }}_k^1\right\}, {\widehat{\lambda }}^1, n \leftarrow 0$   repeat    $n\leftarrow n+1$    for $k=1:K do$     Update ${\widehat{u}}_k$ for all $\omega \ge 0:$
${\widehat{u}}_k^{n+1}(\omega )\leftarrow {\displaystyle \frac{\widehat{f}\left(\omega \right)-\sum _{i<k}{\widehat{u}}_i^{n+1}\left(\omega \right)-\sum _{i>k}{\widehat{u}}_i^n\left(\omega \right)+\frac{\widehat{\lambda }\left(\omega \right)}{2}}{1+2\alpha {(\omega -{\omega }_k^n)}^2}}$	(5)
Update ${\widehat{\omega }}_k:$
${\omega }_k^{n+1}={\displaystyle \frac{{\int }_0^{\infty }\omega {\left|{{\widehat{u}}_k}_k^{n+1}\left(\omega \right)\right|}^{2}d\omega }{{\int }_0^{\infty }{\left|{{\widehat{u}}_k}_k^{n+1}\left(\omega \right)\right|}^{2}d\omega }}$	(6)
end for   Dual ascent for all $\omega \ge 0:$
${\widehat{\lambda }}^{n+1} \leftarrow {\widehat{\lambda }}^n+\tau \left(\widehat{f}\left(\omega \right)-{\sum }_k{\widehat{u}}_k^{n+1} \left(\omega \right)\right)$	(7)
until convergence:
${\displaystyle \frac{{\sum }_k‖{\widehat{u}}_k^{n+1}-{\widehat{u}}_k^n ‖\genfrac{}{}{0pt}{}{2}{2}}{‖{\widehat{u}}_k^n ‖\genfrac{}{}{0pt}{}{2}{2}}}<ϵ$	(8)