This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 1 Evaluating the Uncertainty of Digitizing Waveform Recorders Coherently With the GUM Aldo Baccigalupi, Mauro D’Arco, Member, IEEE, and Annalisa Liccardo Abstract— The performance parameters defined in the IEEE Standard 1057–2007 do not specify the standard uncertainty of the reconstruction levels of digitizing waveform recorders. Not knowing the standard uncertainty of the reconstruction levels affects, in turn, the evaluation of the uncertainty of a number of measurement approaches, based on digital signal processing techniques, which utilize the data collected by a digitizing waveform recorder as the input data. A method to evaluate the uncertainty of memoryless waveform recorders embedded in off-the-shelf digitizing oscilloscopes is proposed here. The method is based on an experimental approach that can be carried out anytime the input signal is repetitive, the frequency response of the oscilloscope can be considered flat, and the dynamical effects are negligible. To qualify the proposed method, the uncertainty estimation obtained by applying it in several experiments is compared with that gained by means of a B-type evaluation. Index Terms— Analog-to-digital converters, measurement uncertainty, quantization, randomness, standardization. I. I NTRODUCTION A RECOGNIZED measurement paradigm to estimate the parameters characterizing dynamic systems and/or phe- nomena consists in digitizing the observable quantities and subsequently applying digital signal processing techniques. Typically, all the quantities of interest are eventually trans- duced into voltage signals, and the digitization task is performed by means of digitizing waveform recorders. The digital signal is represented in terms of a record made up of real numbers, i.e., reconstruction levels [1]–[3]. The acquired record is given in input to an algorithm implementing a measurement model. The same model allows estimating the target parameters and their uncertainty by propagating the standard uncertainty of the input data. The propagation task can be performed analytically or else via Monte Carlo simulations; it can be burdensome but basically represents a technicality [4]–[6]. The weak point of such measurement paradigm, largely appreciated for its flexibility and powerfulness, lies in the dif- ficulties to identify the uncertainty affecting the reconstruction levels of the digitizing waveform recorder. The difficulties Manuscript received January 20, 2018; revised February 27, 2018; accepted February 28, 2018. The Associate Editor coordinating the review process was Dr. Dimitrios Georgakopoulos. (Corresponding author: Annalisa Liccardo.) The authors are with the Dipartimento di Ingegneria Elettrica e delle Tecnologie dell’Informazione, Università degli Studi di Napoli Federico II, 80125 Naples, Italy (e-mail: aldo.baccigalupi@unina.it; mauro.darco@ unina.it; annalisa.liccardo@unina.it). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2018.2815433 originate from the lack of harmonization between the IEEE Standard 1057–2007 [7] and the JCGM 100–2008 docu- ment [8], known as guide to expression of uncertainty in measurement (GUM). The first defines terminology and test methods to synthetically express the quality of digitizing wave- form recorders and allow objective comparisons between their performance. The second instead provides general guidelines to evaluate and express the uncertainty of the measurement results. Unfortunately, the IEEE Standard 1057–2007 neither includes the standard uncertainty of the reconstruction levels among the performance parameters nor highlights its relation with them. The user can, therefore, feel free of quantifying the uncertainties of digitizing waveform recorders data according to his viewpoint [9]–[11]. In a number of applications, the adopted waveform recorders are embedded into digitizing oscilloscopes, and, among the others, the following very frequent behaviors can be observed. The systematic errors, namely, offset, gain error, and non- linearity, are almost never measured and compensated, despite they play a dominant role, especially in the presence of narrowband signals acquired in quasi-static operating condi- tions [12]–[14]. Off-the-shelf digitizing oscilloscopes, in fact, do not allow trimming of any complementary hardware to perform compensation. Nonetheless, the implementation of postprocessing techniques, such as dithering, is avoided due to the related burdensome impact [15]–[17]. The unknown systematic errors are, instead, assimilated to uncertainty contri- butions, which are quantified according to a B-type evaluation method, taking into account the dc accuracy specified in the oscilloscope datasheet [18]–[20]. In the presence of broadband signal acquired in highly dynamic conditions, a very common approach consists in deriving the uncertainty of the reconstruction levels from the signal-to-noise-and-distortion ratio, by equating it to the rms value of the noise and distortion contributions [7], [21], [22]. This approach assigns the same uncertainty value to every reconstruction level, which is a rough simplification of a multifaceted problem [23]–[25]. Also, it is not unusual that the uncertainty value assigned to the reconstruction levels of the adopted waveform recorder is gained by combining an arbitrary subset of all the performance parameters listed in the IEEE Standard 1057–2007 [7]. The measurement report is then complemented with some discus- sion to support the adopted viewpoint [26]–[28]. Although subjective evaluations are not denied by GUM guidelines, these should be limited to measurement processes where 0018-9456 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.