## 1 Introduction  
The measurement channels of modern measurement and control equipment typically include components that perform digital processing of measurement signals [1, 2, 3, 4]. This approach enables the use of a wide range of signal processing algorithms to extract useful information [5, 6, 7], apply multiplicative algorithms for power and energy measurements [8, 9], analysis of power grids fails and short circuits [10, 11], or perform static and dynamic reproduction of processed quantities [12, 13, 14, 15]. Although the most important operations related to signal processing are performed digitally, the physical quantity being measured is continuous in time and must first be converted into an electrical voltage. This voltage--after being processed by the analog part of the measurement chain--is then converted into digital form by an analog-to-digital (A/D) converter. This process is shown in Figure 1.  
Figure 1: Diagram of a typical implementation of a measurement chain (source [16] under the CC BY 4.0 license). The analysis of the inaccuracy in determining the values of the output quantities of the measurement chain must therefore include a description of the analog processing, which ultimately allows for estimating the uncertainty budget of the input quantities of the A/D converter [14; 17]. The next stage of the analysis is to determine the impact of the A/D conversion process on the error signals present in the output quantities of the A/D converter. The final stage is to determine the metrological properties of the digital processing algorithm (D/D). This approach has been successfully used, among others, in [14; 16; 18; 19; 20]. According to the proposal presented in the literature [14; 19; 21] for dividing error signals, it can be observed that the parameters of some of the above-mentioned signals are closely correlated with the waveform of the signal representing the measured physical quantity. As shown in [13; 16; 18; 19; 22; 23], the dynamic error signals resulting from the imperfect transmittance of subsequent fragments of the measurement chain are closely related to the spectrum of the signal processed by the chain. Imperfect transmittance is understood as one that deviates from that assumed by the designer of the measurement chain [23]. In practice, this means that the development of the uncertainty budget of the output quantities of the measurement chain is not possible without knowing or estimating the spectrum of the input quantity processed by it. Currently, no method has been proposed in the literature that allows estimation of the parameters of the discussed error signals without knowledge of the properties of the processed signal. To address the above-mentioned problems, this article proposes a method for estimating the parameters of the dynamic error signal of the input quantities of the digital part of the measurement chain based on the spectrum of these quantities and the error model of the analog part of the chain. The presented analysis includes various cases in which typical problems of the method are discussed and its effectiveness is demonstrated. In addition to simulation results, the article presents an example of the application of the proposed method to an exemplary measurement chain and provides the results of a measurement experiment verifying the effectiveness of the method. The article is a continuation of the considerations contained in [16; 18]. The paper is divided into six sections. Section 1 discusses the current state of knowledge on the subject and presents the general concept of the work. Section 2 is devoted to the discussion of the mathematical model of the error signal, where the most important dependencies and derivations are presented. In Section 3, a proposed method for estimating the error signal parameters, discussed in Section 2, is presented. Sections 4 and 5 are devoted to simulation and measurement verification of the proposed method, and examples of its application are indicated.