## 3 Results
### Test of SF Algorithm with PTB Diagnostic ECG Database
#### 3.2.5 Test 5: PLI linear Frequency Change  
The test design of PLI linear frequency change in Table 2 simulates 10 different slew rates of the PLI frequency \(\Delta f_{PLI}\) = \(\pm\)(0.01, 0.025, 0.05, 0.075, 0.1 Hz/s), where positive and negative signs indicate tests with an increasing or decreasing PLI frequency from the nominal \(f_{PLI}\) = 50 Hz, covering a maximal span of 49-50 Hz and 50-51 Hz over 10 s. Our preliminary observation of RMSE, MAXE, and \(SNR_{imp}\) led to the conclusion that there are not substantial differences between positive and negative sign tests; therefore, Figure 15 reports the statistical evaluation of all the performance metrics combined for \(\pm\Delta f_{PLI}\).  
Figure 15a shows that SF errors remain stable regardless of the slew rate of the dynamic PLI frequency change. We note a relatively narrow span of median values (min-max ranges) of RMSE = 1.5-1.8 \(\upmu\)V (1.2-4 \(\upmu\)V) and MAXE = 6.2-8.1 \(\upmu\)V (4.6-14 \(\upmu\)V) for all 12 ECG leads. The improvement in SNR is also weakly dependent on the frequency slew rate (Figure 15b), presenting a narrow span \(SNR_{imp}\) = 57.2-58.5 dB, which is noted to be in the same range as the constant frequency test (Test 2) in Figure 11. We can therefore conclude that the performance of the SF algorithm is weakly influenced by any kind of PLI frequency change in the range of 48-52 Hz, introducing a maximal error of \(<\)15 \(\upmu\)V in any ECG lead and any ECG record of the test database. Such error levels are practically invisible as QRS or ST distortions in the filtered 12-lead ECG plot in Figure 16b; although, the ECG signal with the superimposed PLI (\(\Delta f_{PLI}\) = 0.1 Hz/s and amplitude 1000 \(\upmu\)V r.m.s.) is diagnostically unreadable before filtering in Figure 16a. Although the provided y-scaling of leads is adjusted without inter-lead overlap, any output distortions are likely not to be noticed in augmented amplitude scales too.  
Figure 13: SF algorithm performance for PLI linear amplitude change, computed for 10 s 12-lead ECG from the PTB Diagnostic ECG database and added PLI sinusoid with settings according to Table 2 (Test 4). The boxplots (median; box: 25–75%; whisker: min–max) represent: (**a**) MAXE and RMSE, (**b**) \(SNR_{imp}\) ordered for 12 ECG leads (from left to right); I, II, III, avR, avL, avF, V1, V2, V3, V4, V5, V6.  
Figure 14: Example of 10 s 12-lead ECG trace (s0546_re.dat from PTB Diagnostic ECG database) shown in a grid (200 ms/div, 500 uV/div): (**a**) 12-lead ECG superimposed by PLI (50 Hz) with linearly changing amplitude over 10 s at the extreme slew rate (200 uV/s); (**b**) filtered 12-lead ECG by SF algorithm with 10\(\times\) zoomed segment of lead I (1 s, 50 uV/div), showing the overlap between original ECG (red) and filtered ECG (green). The y-scaling of 12 ECG leads retains no inter-lead overlap; thus, ECG in (**b**) is a zoomed-in representation of (**a**) after filtering of the large PLI component.  
Figure 15: SF algorithm performance for PLI linear frequency change, computed for 10 s 12-lead ECG from the PTB Diagnostic ECG database and added PLI sinusoid with settings according to Table 2 (Test 5). The boxplots (median; box: 25-75%; whisker: min–max) represent: (**a**) MAXE and RMSE, (**b**) \(SNR_{imp}\) ordered for 12 ECG leads (from left to right): I, II, III, avR, avL, avF, V1, V2, V3, V4, V5, V6.