Calculation of Pulse Parameters and Propagation of Uncertainty

The fundamental starting point for the analysis of all two-state waveforms is the determination of the low- and high-state levels. This is a two-step process. First, the data are grouped into points belonging to each state, and second, the value of each state is determined from the group mean, the mode, the median, or some other statistic. Once the state levels are determined, pulse parameters such as transition duration, amplitude, overshoot, and undershoot can be calculated. The IEEE 181-2003 Standard on Transitions, Pulses, and Related Waveforms recommends methods for grouping the data, determining the state levels, and determining pulse parameters, but gives no guidance for propagation of uncertainty, particularly in the presence of systematic and/or correlated sources of error. Correlations are important because certain pulse parameters, such as transition duration and pulse duration, are invariant with respect to, e.g., multiplicative error, which is correlated highly. We propose a new procedure for determining the pulse states that involves clustering the data and then using a robust location estimator to determine the state level. This technique allows the propagation of uncertainty from the covariance of a sampled waveform representation all the way to the calculation of pulse parameters. We use Monte Carlo simulations to verify the proposed procedure for some canonical pulse waveforms.