Abstract
The paper presents considerations concerning the transfer of random errors from the input to the output of the Discrete Wavelet Transform (DWT) algorithm. The concept of determining an uncertainty of its output data based on the probabilistic error description has been presented. The DWT is discussed as the product of the vector of input quantities and the matrix of algorithm coefficients. Calculations of the uncertainty of a single output result of the algorithm are described with assumption that the input quantities are burdened by random errors of known distributions. Theoretical considerations have been verified by simulation experiments using the Monte Carlo method. Determining the uncertainty at the DWT output is possible due to the specific properties of transferring random errors by linear and additive algorithms.
Highlights
Digital data processing algorithms are an indispensable part of most measurement systems [1]
For decomposition levels 2 and 4 it is about 1 (1.027, 1.026), for higher levels, 6 and 8, it is less than 1. This means that for this family of wavelets, random errors are not amplified from input to output of the Discrete Wavelet Transform (DWT) algorithm, and for higher levels of decomposition, these errors are suppressed
The presented method of calculating the uncertainty of the DWT algorithm output quantities, described for the universal case in [6,7,18], gives results similar to those obtained in the simulation
Summary
Digital data processing algorithms are an indispensable part of most measurement systems [1]. Due to the large complexity, the analysis of properties of measuring chains containing elements of digital data processing is often omitted in many systems focused on wavelet transform applications [2,3]. This article will describe the general signal processing structure, bases of wavelet transform algorithm and its matrix After introducing this elements-uncertainty calculation method will be described. The numerical operation performed by a data processing algorithm can be presented in the matrix form [7] For this purpose, it is necessary to identify the algorithm coefficients. In the case of an analytical approach, any modification of algorithm parameters such as mother wavelet, decomposition level, number of input samples, requires problem re-analysis This situation is problematic in a measuring chain design because these parameters are changed in the design process and the uncertainty analysis must be repeated. The method described in this paper enables the analysis of any combination of the filter bank and requires only identification of the algorithm coefficients matrix
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