Algorithm 1.

Bivariate EMD

1:  Let $\tilde{z}(t)$=z(t),

2:  a unit complex number $e^{-j{\theta }_k}$ is used to project the complex signal $\tilde{z}(t)$ in the direction of θk to obtain K signal projections, given by $$p_{{\theta }_k}(t)=\Re (e^{-j{\theta }_k}\tilde{z}(t)),k=1,\dots ,K$$ where ℜ(.) represents the real part of a complex number, and θk = 2kπ/K,

3:  locate ${\left\{t_j^k(t)\right\}}_{k=1}^K$ corresponding to maxima points of ${\left\{p_{{\theta }_k}(t)\right\}}_{k=1}^K$,

4:  obtain envelope curves ${\left\{e_{{\theta }_k}(t)\right\}}_{k=1}^K$ by using the spline interpolation of maxima points $\left[t_j^k,\tilde{z}(t_j^k)\right]$,

5:  determine the arithmetic mean m(t) of all envelope curves, and subtract from the input signal i.e., $d(t)=\tilde{z}(t)-m(t)$. Next, let $\tilde{z}(t)=d(t)$ and go to step 2,

6:  repeat until d(t) becomes an IMF.