Full information from measured ADC test data using maximum likelihood estimation

ADC testing is often done using sine wave excitation (see e.g. IEEE standard 1241). A sine wave is fitted to the measured data in least squares sense, and the residuals are analyzed further. In recent papers, it has been recognized that even more (and more precise) information can be extracted by the solution of the maximum likelihood equations. This is an improvement to the usual three-parameter and four-parameter fits. In this paper practical implementation of this algorithm is suggested. Then, theoretical background is over-viewed. Further investigations lead to the statement that the same principle can be extended to any measurement which uses an excitation signal which can be described with a few parameters. A candidate for this is an exponential signal, with three parameters: e.g. start value, end (steady-state) value, and time constant. The maximum likelihood (ML) equations yield a solution for these too, more accurate than least squares (LS) fitting. Reasonable approximations make the ML problem solvable in practice. (C) 2011 Elsevier Ltd. All rights reserved.