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The article presents a method for analyzing the own errors of the discrete wavelet transform algorithms, which are introduced by these algorithms into the output quantities. The presented considerations include determining the origin of the error signals in question and determining their parameters. Both errors resulting from imperfections in the transmittance of the algorithm and those resulting from its implementation in the actual measurement chain were considered.

The article describes a method for determining the resultant expanded uncertainty value in the case of analyzing an uncertainty budget with many components. It employs interval arithmetic, known for its low calculation complexity compared to other methods in the literature. The article includes a detailed explanation of the proposed method and showcases its applications. Results are compared with those from the Monte Carlo method and assumptions based on the central limit theorem. The relative error in estimating the resulting expanded uncertainty value typically stays within ±5% of the Monte Carlo method’s result.

This paper presents an error model of a measurement chain containing a link that executes a discrete wavelet transform algorithm, which is most often the last stage of measurement signal processing. The goal is to determine the uncertainty budget of the input quantities of the wavelet transform algorithm. The error model takes into account parts of analog, analog-to-digital and digital processing, describing the properties of subsequent fragments of the chain using their transmittance and processing functions. The proposed model enables the description of both the deterministic and non-deterministic properties of signal errors. The proposed model was validated using an example measurement chain created for this purpose.

This paper discusses the role of the discrete wavelet transform algorithm in processing error signals present in the input quantities of the algorithm. In considering the error model of the measurement chain, the parameters of the error signals in the input quantities of the wavelet transform algorithm are estimated. Subsequently, in accounting for the algorithm’s properties, the parameters of its output values are determined, and the resulting uncertainty values of the output quantities of the measurement chain are estimated. The interval reduction arithmetic method is employed in the calculations for estimating the expanded uncertainty. All findings were validated through measurements conducted using the implemented measurement chain.