# Error Model of a Measurement Chain Containing the Discrete Wavelet Transform Algorithm
## 5 Reasons for Discrepancies in Results  
Based on the results presented in Tables 1 and 2, as well as on the basis of Figure 5, it can be noticed that the results obtained from the measurement experiment are not perfectly consistent with those obtained analytically. The main reason for the discussed discrepancies is the inaccurate determination of the parameters of the error model of the input quantities of the WT algorithm.  
The measurement experiment carried out, the aim of which was to identify the static properties of the analyzed section of the measurement chain, assumed that the input values of the measurement chain were not encumbered with any errors. This simplification is inappropriate, and its elimination would require an identification of the properties of the arbitrary waveform generator used, which has not been carried out. Unfortunately, due to insufficient information being contained in the instrument documentation, the properties of the generator have to be determined experimentally.  
In the case of dynamic properties, a discrepancy between the actual and estimated value of the phase shift \(\varphi_{y}\) introduced by the analyzed measurement amplifier can be noticed. Figure 6 shows the measured and estimated values of the quantity in question based on Equation (56). In order to improve the obtained results, a higher order polynomial or a better model describing the properties of the measurement amplifier should be used.  
The last simplification requiring discussion is the omission of the analysis of static error signals. As the experiment was performed under constant ambient conditions, the error signals in question did not occur. In reality, however, an appropriate measurement experiment should be carried out to identify them. For example, in the case of zero drift of the measurement amplifier and ADC converter, the influence of the ambient temperature on the introduced drift should be determined. Determining the parameters of the error signal in question enables its analysis in accordance with the method presented earlier in the work.  
As the aim of the work was to indicate how to quantitatively describe the metrological properties of the measurement chain using the proposed error model, the work did not focus on a very precise determination of the parameters of the discussed model. In fact, the designer of the measurement chain should identify all error sources and indicate their parameters as precisely as possible. As there are works devoted to the analysis of subsequent fragments of the measurement path (e.g., in case of ADC works such as [22; 24; 25]),  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Frequency \(f_{s,o}\), Hz** & **Measured \(\sigma_{m}^{2}\), mV** & **Calculated \(\sigma_{c}^{2}\), mV** & **Relative Error \(\delta\), \%** \\ \hline
1000 & 1.20 & 1.31 & 9.23 \\
2000 & 5.31 & 4.95 & \(-\)6.75 \\
3000 & 10.06 & 11.06 & 9.93 \\
4000 & 21.20 & 19.49 & \(-\)8.08 \\
5000 & 34.34 & 29.58 & \(-\)13.85 \\ \hline \hline \end{tabular} Mean of absolute relative error values is equal to 9.5\%  
\end{table}
Table 2: Experimentally determined \(\sigma_{m}^{2}\) and estimated \(\sigma_{c}^{2}\) values of the variance in the resultant error signal \(e_{x,\Sigma}(i)\), where the symbol \(\delta\) denotes the relative error of estimating the variance of the analyzed error signal (in the case of a polyharmonic input signal).  
this work focused on an example with a minimum degree of complexity, while presenting results with an acceptable error.