IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 50, NO. 5, OCTOBER2001 1355 An Identification Technique for Data Acquisition Characterization in the Presence of Nonlinear Distortions and Time Base Distortions Gerd Vandersteen, Member, IEEE, Yves Rolain, Senior Member, IEEE, and Johan Schoukens, Fellow, IEEE Abstract—The nonlinear behavior of data acquisition channels and analog-to-digital converters is often measured using sine-wave measurements. High-frequency sampling scopes also suffer from time base distortions. This implies that the signals are sampled at a nonequidistant time grid. This paper describes a robust and efficient identification technique to characterize acquisition chan- nels which suffer from both nonlinear distortions and/or time base distortions in the presence of both additive and jitter noise. An automatic model selection scheme and the generation of uncer- tainty bounds are obtained through the statistical properties of the proposed simulator. The applicability of the method is demon- strated on both simulations and measurements of high-frequency sampling scopes. Index Terms—Analog–digital conversion, data acquisition, max- imum likelihood estimation, nonlinear distortion, parameter esti- mation, timing jitter. I. INTRODUCTION D ATA acquisition channels suffer from different kinds of nonidealities which are characterized and measured in various ways [1]. Existing methods often characterize the different types of distortions separately using sine-wave fitting procedures [1]–[5]. This implies implicitly that the other distor- tions are assumed to be negligible during the characterization. In order to strengthen the characterization of a data acquisition channel, all distortions which interact with each other should be estimated simultaneously. The proposed technique is especially suited for high-fre- quency sampling scopes, which suffer from both nonlinearities (due to the nonlinear behavior of the high-frequency sampling diodes) and from time base distortions. The latter distortions can be introduced by imperfections in the time base generation of equivalent time principle-based scopes [6]. The method is applied on both simulations and measurements of high-fre- quency sampling scopes. Manuscript received February 22, 1999; revised April 20, 2001. This work was supported by the Belgian Fund for Scientific Research—Flanders (FWO—Vlaanderen), the Flemish government (GOA-IMMI), and the Belgian government as a part of the Belgian program on Interuniversity Poles of Attraction (IUAP 4/2) initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. G. Vandersteen is with IMEC/DESICS, B-3001 Leuven, Belgium (e-mail: Gerd.Vandersteen@imec.be). Y. Rolain and J. Schoukens are with the Electrical Measurement Depart- ment, Vrije Universiteit Brussel, B-1050 Brussels, Belgium (e-mail: Yves.Ro- lain@vub.ac.be; Johan Schoukens@vub.ac.be). Publisher Item Identifier S 0018-9456(01)08097-4. The aim of this paper is to provide a robust and efficient iden- tification algorithm to identify the nonlinear distortion and the time base distortion of a data acquisition channel using sine- wave measurements (Section II). An automatic model selection scheme and the generation of uncertainty bounds are obtained through the statistical properties of the proposed simulator. The proposed technique is compared with existing methods [1], [2], [4], [5] on simulations (Section III) and measurements (Sec- tion IV). Section V demonstrates some practical applications of time base compensation on measurements. II. IDENTIFICATION ALGORITHM After introducing the signal model of and the assumptions on the perturbations, a maximum likelihood (ML) estimator is derived. A model selection criterion is given based on the sta- tistics of the ML cost. Furthermore, a numerically efficient way to compute the minimizer of the cost is presented. Afterwards, the statistical impact of replacing the exact (but unknown) noise variances with the measured sample variances is discussed. A. Signal Model The signal model must describe the physical signal as closely as possible. This reduces the modeling errors and therefore in- creases the precision of the results. Precision sine-wave gener- ators often use some frequency locking techniques in order to derive the desired frequency out of a stable reference frequency. It is therefore assumed that the output frequency of the gener- ator is exactly known. Harmonics of the fundamental frequency are inevitably generated by the output amplifier and/or the data acquisition channel. For that reason, the following signal model is proposed. Assumption 1: The continuous-time signal model for the measurements of the th experiment is given by (1) where time variable; (known) fundamental pulsation; and (unknown) amplitudes of the th harmonic. The set of harmonics can be vary from measurement to mea- surement depending on the number of harmonics that can be detected in the measured signal. The number of harmonics, rep- resented by , is assumed to be finite. 0018–9456/01$10.00 © 2001 IEEE