Algorithm 1.

Proposed PCA method

1: Estimate variance of signal (diagonal of $\widehat{\Sigma }$) using eq. (10), and estimate SNR proxy

2: Add all frequencies ${\xi }^k$ to considered set $C$

3: for it = $1\dots d$ do

4:  Select $i^{*}$, the largest SNR $\left({\xi }^k\right)$ proxy in $C$

5:  Add $i^{*}$ to selected set $S$

6:  Remove all $j$ such that $\left|{\xi }^j-{\xi }^{i^{*}}\right|<2$ from $C$

7: end for

8: Estimate all columns in $S$ using eq. (10) and their complex conjugates to form ${\widehat{\Sigma }}_{\text{col}}$

9: Orthogonalize ${\widehat{\Sigma }}_{\text{col}}$ and store in $\tilde{U}$

10: Compute the reduced covariance matrix ${\widehat{\Sigma }}_{\tilde{U}}$ using eq. (14)

11: Compute the eigenvalue decomposition of ${\widehat{\Sigma }}_{\tilde{U}}=V\Gamma V^{*}$

12: Return principal components $U≔\tilde{U}V$, eigenvalues $Г$