# Feasibility of Low Latency, Single-Sample Delay Resampling: A New Kriging Based Method
## 4 Results
### Single-Delay Scenario  
All methods, except for Akima, required higher OSR to achieve the same SNR, after switching to the single-delay scenario (Figure 10). Akima always required three future samples for both group- and single-delay scenarios. The other methods were only allowed to use one future sample.  
The RMSE for Margolis showed significant oscillations, with negative peaks every 0.05 Hz. Margolis provides perfect reconstruction of recurrent signals, which explains the low error if the input window length is a multiple of the signal interval. The window length was defined in samples, which led to slightly varying length in time units in case of jitter. Therefore, an exact match with the signal interval and perfect reconstruction was not fully achieved.  
Figure 9: Comparison of Kriging, Margolis, Lagrange, and Akima interpolation for jitter (solid lines, first OSR value in legend) and missing samples (dashed lines, second value) in the group-delay scenario. Clean signals (**a**) and signals with noise of \(-60\) dB added (**b**). WSI only tested for uniform and missing samples without noise.  
Apart from those oscillations, Margolis and Kriging achieved similar RMSE values, with a slight advantage for Kriging at the threshold of \(E_{Max}=-40\) dB. The necessary OSR to resample jitter signals by Kriging was 8% lower compared with Margolis, 39% compared with Lagrange, and 65% compared with Akima.  
In comparison with the group-delay scenario, the OSR had to be increased by a factor of 1.4 for Margolis, by a factor of 1.6 or 1.7 for Kriging, and by a factor of 2 for Lagrange to achieve at the threshold of \(E_{Max}=-40\) dB. For a threshold of \(-60\) dB, a factor between 1.5 and 2.2 was necessary.  
Comparing jitter and missing samples in the single-delay scenario showed that a between 10% and 22% higher OSR was necessary in the latter case. The percentage increase of the OSR was higher, as it also was in the group-delay scenario.  
The OSR was only slightly increased by quantization (Figure 11a). Apart from this, the single-delay scenario was highly sensitive towards noise. If the input signal was truncated to a resolution of 12 bits, only Akima came close to the equivalent noise floor of \(-78.2\) dB. The other methods had RMSE values between 12 dB and 23 dB above the input noise. In case of missing samples, it was not possible to achieve at a lower error threshold of \(E_{Max}=-60\) dB.  
If a higher noise amplitude of \(-60\) dB was added to the input signal, Kriging and Margolis showed dissimilar behaviour (Figure 11b). Kriging was better for signals with  
Figure 11: Effect of quantization to 12 bit (**a**) and of adding \(-60\) dB noise (**b**) to the single-delay scenario with jitter (solid lines) and missing samples (dashed lines).  
Figure 10: Single-delay scenario for jitter (solid lines) and missing samples (dashed lines) without noise. Comparison of Kriging, Margolis, Lagrange, and Akima interpolation.  
lower frequencies with \(f_{L}<0.19\) Hz. The lowest RMSE values were 2.7 dB above the noise floor, whereas Margolis remained 13 dB above the noise floor. Above \(f_{L}>0.19\) Hz, Margolis was the more accurate method for jitter signals, with a 17% lower OSR. However, Margolis failed to provide satisfactory interpolation in case of missing samples. Only Kriging and Akima achieved at an RMSE below \(-40\) dB.