**5. Results**

To generate comparable results, all compression approaches are set on a CR round about 4:1. This CR is like a trade-off between the advantages of compression and sufficiently high data fidelity, but randomly chosen for this test case. Although higher CRs are technically possible, this is not the objective of this paper. A comparison of all results for the compression of *U*Noise and *I*DS is displayed in Table 1.

**Table 1.** Compression factor, MAE and processing time of different compression approaches for *U*noise and *I*DS.


The proposed approaches have been implemented using MATLAB and performed on a PC Intel core i5-3210M processor, 2.50 GHz, with 4 GB of RAM. To illustrate the difference between the approaches, Figures 8 and 9 show the resulting decompression graphs for *U*Noise and *I*DS. In particular, the TFA algorithm does not possess good compression properties, especially when looking at Figure 9. The original curve is simply linearized because of a sluggish (high) threshold (±m*σ*), even if the resulting MAE is as good as in the other compression methods.

Only the WT and SVD algorithms yield accurate values for the impedance after the recombination of *U*base and the decompressed *<sup>U</sup>*noise(DC) including the decompressed current *<sup>I</sup>*DS(DC). WT shows a particularly good fit of its decompressed impedance values *Z* to the original values *Z*1 (Figure 10). Based on (10), Figure 10 shows the absolute impedance |*Z*| (a), the impedance angle ∠(*Z*) = *ϕ*Z (b), and the absolute deviation Δ |*Z*1 − *Z*| (c) over the frequency *f* .

*Z* = |*Z*| *ϕ*Z (10)

**Figure 8.** Comparison of *U*DS and the resulting compression outputs ∑(*<sup>U</sup>*base , *<sup>U</sup>*noise(DC)) of the different lossy approaches.

**Figure 9.** Comparison of *I*DS and the resulting compression output of the different lossy approaches *<sup>I</sup>*DS(DC).

Only for frequencies ≥ 25 kHz do the discrepancies in the WT results increase slightly ( ≥1%), see Figure 10 (bottom). In comparison see Figure 11, the results obtained by the SVD algorithm deviate from the original dataset by almost 2% for f ≥ 25 kHz. Depending on *I*DS, the TFA algorithm produces a large deviation of the MAE that leads to the significantly worse results.

Additionally, both the SVD and the TFA algorithms show high processing times *<sup>t</sup>*(*I*), *t*(*U*) (Table 1). An evaluation of the best fitting technique based on the processing time is only possible to a limited extent. Compression using SVD and WT should be investigated for each data set separately. Conclusively, the TFA algorithm is deemed inadequate to handle the task discussed in this paper or similar tasks.

**Figure 10.** Impedance measurement results of the original (ori = original dataset and their impedance *Z*1) and decompression results using WT (WT = WT decompressed dataset and their impedance *Z*). The absolute impedance |*Z*| (**a**), the impedance angle ∠(*Z*) = *ϕ*Z (**b**), and the absolute deviation Δ |*Z*1 − *Z*| (**c**) over the frequency *f* are shown.

**Figure 11.** Impedance measurement results of the SVD, for explanation see Figure 10.
