# Error Model of a Measurement Chain Containing the Discrete Wavelet Transform Algorithm
## 6 Conclusions  
Based on the results listed in Tables 1 and 2 it can be seen that the estimated values of the variance in the resulting error signal of the input quantities of the DWT algorithm are close to those obtained by measurement. The proposed error model for the measurement chain allows to describe both deterministic and random error signals, and the parameters of these signals can be identified by measurement, as shown in the example presented. The example of a monoharmonic signal presented in this paper is the most simplified case, due to the presence of only one component of the dynamic error signal (in the discussed case, the dynamic error signal contains only one harmonic component). In the case of a polyharmonic signal, an example is presented in which a triangular signal was processed to indicate how to analyze many harmonics of the dynamic error signal and, therefore, many components of the resultant error signal of the output quantities. The presented analysis is performed identically for signals with any spectrum.  
The application of the error model described in the article is simplified and does not take into account, among other things, error signals occurring in the input value of the measurement chain. The presented error model allows for a full analysis, while the adopted simplifications were justified by the need to present an example with a minimum degree of complexity. For the same reason, the analysis of static error signals was omitted. The mean of the absolute relative error values of the analyzed error signal was less than 10%, which means that a standard uncertainty value of relative error should be less than 5%. To improve accuracy of estimating discussed values a more precise measurement chain model parameter values must be obtained.  
The example provided may constitute a set of guidelines for designers of measurement chains using WT algorithms on how to describe the metrological properties of the measurement chain so that a further analysis of the impact of these algorithms on the identified error signals is possible. The last step necessary to determine the uncertainty value of the output quantity of the measurement path presented in this work is to indicate how the analyzed WT algorithm affects the error signals identified in this article and present in the input quantities of this algorithm. The mentioned analysis was not presented in the current paper and is a separate issue, which will be discussed in subsequent works. Regardless of the number of error signals analyzed and the number of subsequent processing stages occurring in the measurement chain, the application of the presented error model is identical and its level of complexity does not change.  
Figure 6: Measured and estimated (according to the Equation (56)) values of phase shift \(\varphi_{y}(\omega)\) introduced by amplifier.  
**Author Contributions:** Methodology, M.K.; Software, L.D.; Validation, M.K. and J.R.; Formal analysis, M.K.; Investigation, L.D.; Resources, L.D.; Data curation, L.D.; Writing--original draft, L.D.; Writing--review & editing, M.K. and J.R.; Visualization, L.D.; Supervision, J.R.; Project administration, M.K. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was partially funded by the Polish National Science Centre (NCN) grant number 2022/47/B/ST7/00047 and by Rector of Silesian University of Technology grant number 05/020/RGJ24/0084.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Conflicts of Interest:** The authors declare no conflicts of interest.