## 8 Experimental Results
The low-frequency value used was 10 Hz, and the high-frequency value used was 10 kHz. Figure 13: Chart containing the experimentally estimated sinewave standard deviation as a function of the injected amount of phase noise. The number of data points used was 500, and the confidence level used was 99.9%. The values obtained for the different function generator settings of phase noise modulation are the ones represented in Figure 14 using, again, error bars to represent the confidence intervals for the same 99.9% confidence level and 50 repetitions (\(n=50\)). The low-frequency value used was 10 Hz, and the high-frequency value used was 10 kHz. The amplitude was 900 mV, and the number of acquired samples was 100 at a rate of 100 kHz. We are thus now able to represent the estimated amplitude standard deviation as a function of jitter. This can be seen in Figure 15. The vertical and horizontal error bars represent the confidence intervals for the estimated sinusoidal amplitude and jitter, as shown in the previous two figures. One can observe a linear relationship between the two variables, as expected from Equation (28). A straight line was fitted, in a least squares sense, to the data points, and the following relation was obtained:  
\[\sigma_{A}=2328.373[\mathrm{V}/\mathrm{s}]\cdot\sigma_{t}-21.185\cdot 10^{-6}[ \mathrm{V}] \tag{34}\]  
Comparing this with the expected relation given in (28), one obtains  
\[\sigma_{A}\approx\frac{0.9[\mathrm{V}/\mathrm{s}]}{\sqrt{2\cdot 100}}\cdot 2 \pi\cdot 5000\cdot\sigma_{t}\cdot K \tag{35}\]  
with  
\[K\approx 1.16 \tag{36}\]  
This straight line is depicted in Figure 15 using the dotted trace. A discrepancy was found between the slopes of the analytical and experimental relationships. This discrepancy is given by the coefficient \(K\approx 1.16\), which was expected to be \(K=1\). This 16% discrepancy may be due to several phenomena. The method used to measure the amount of jitter introduced was the one suggested in the standard IEEE 1057. This method assumes that when the stimulus signal frequency changes (10 Hz and 10 kHz were  
Figure 15: Experimental estimated amplitude standard deviation as a function of sampling jitter present. The error bars represent the confidence intervals for the estimation of both the amplitude estimation carried out with the least squares sine fitting method and the estimated amount of jitter present. The dashed line represents the straight line that best fits the data points. The number of data points used was 500, and the confidence level used was 99.9%. used), the sinewave generated has all the same properties, apart from frequency. It assumes that the sinewave amplitude remained the same, which is not guaranteed. Furthermore, the stimulus signal is \"filtered\" by the frequency response of the data acquisition board. This response might not be perfectly flat for those frequencies. Another problem is that the sinewave generated might have some harmonic distortion, and thus the energy inside the bandwidth of the data acquisition board might be different for the two frequencies. This discrepancy should be the subject of future research to better understand its origin.