# Feasibility of Low Latency, Single-Sample Delay Resampling: A New Kriging Based Method
## 4 Results
### Influence of Window Length and Kriging Range  
Additional simulations were also performed to evaluate the impact of the window half-width and Kriging range on \(f_{40}\) (Figure 7). When selecting the values of HW and \(r\) other factors must also be considered, such as a flat frequency response, ensuring reasonable CPU time, and maintaining mathematical stability.  
The noise sensitivity of the different methods was tested in additional simulations. White noise with \(\sigma=1\) was used as input signal. Depending on the resampling method and the window width, the output contained amplified noise and aliasing frequencies. The relation of the root mean square amplitudes (RMSA) between the resampled output signal and the noise input signal was calculated. The relation showed how distortions by noise are amplified by the different methods (Figure 8). Kriging was tested for two variogram parameter sets, including zero nugget and \(n_{g}=10^{-6}\). Further analysis of the nugget follows in Section 4.4.  
Figure 6: Reconstruction error for uniformly sampled signals as function of sine–wave frequency. RMSE for centre (solid lines) and margins (dotted lines) of available time window. OSR for E\({}_{\text{Max}}=-40\) dB (centre of time window).  
Akima was the only method that slightly reduced the noise amplitude by \(-0.6\) dB. However, it can only operate with a fixed HW of three. The noise sensitivity of Margolis and Lagrange increased with the HW. Kriging provided an almost constant moderate noise amplification of 0.8 dB for group- and 2.4 dB for single-delay. The nugget value must be included in the variogram for the single-delay scenario; otherwise, the noise sensitivity also increases with HW for Kriging.  
HW was set to the values with the highest \(f_{40}\) for the group-delay scenario, i.e., HW = 20 for WSI, HW = 18 for Lagrange/Margolis, and HW = 25 for Kriging. Lower HW values are preferred for the single-delay scenario to reduce CPU time and noise sensitivity. Values of HW = 10 for Lagrange/Margolis and HW = 20 for Kriging were selected. These values also provided a good accuracy regarding a lower error threshold of \(E_{Max}=-60\) dB. Margolis and Lagrange are both highly noise sensitive; higher HW values should be avoided. WSI did not yield satisfactory accuracy in the single-delay scenario regardless of HW.  
The Kriging range was set to \(r=6\cdot T_{S}\) for the group-delay scenario. The higher average sampling interval of \(T_{S}=1.1\) s for the case of missing samples corresponds to \(r=6.6\) s. A slight increase of the range for the single-delay scenario to \(r=6.5\cdot T_{S}\), equivalent to \(r=6.5\) s for uniform and jitter, and \(r=7.15\) s for missing samples, led to higher \(f_{40}\) values.  
Figure 8: Noise sensitivity as function of window half width. Amplification of white noise amplitude by different resampling methods. Group-delay (**a**) and single-delay (**b**) scenarios.  
Figure 7: Effect of window half-width and Kriging range on the frequency limit \(f_{40}\). (**a**) HW test for WSI (uniform) and Margolis. (**b**) HW test for Kriging r = 6\(\cdot\)T\({}_{\rm s}\) for group- and single-delay scenarios. Missing samples only tested for single delay. (**c**) Effect of variogram range.