Oscilloscopes are routinely used to measure the properties of a wide variety of pulsed waveforms, including digital data streams in computers and in electrical and optical communications. Accurate characterization of pulse parameters and their measurement uncertainty has a huge economic impact on the producers and the consumers of the digital communications equipment and computers that are ubiquitous in modern everyday life. With cost pressures driving manufacturers to create products that just meet specifications, the ability to make robust and well-characterized measurements is becoming more important. In a recent issue of IEEE Transactions on Instrumentation and Measurement, NIST researchers Paul Hale (EEEL Optoelectronics Division) and C.M. Jack Wang (ITL Statistical Engineering Division) describe a method that can be used to accurately calculate pulse parameters by use of linear transformations on the original waveforms using covariance analysis. Prior to this work, correlated errors were not accounted for in estimates of parameter uncertainties.  Correlations are important because certain pulse parameters, such as transition duration, are invariant with respect to highly correlated errors, such as multiplicative error. This covariance approach is an extremely powerful technique because it can be extended to estimate the uncertainty of any scalar or vector quantity that is derived from the waveform through a suitably linear transformation. This can include time domain, as well as frequency domain quantities.
 Paul D. Hale and C.M. Jack Wang, "Calculation of Pulse Parameters and Propagation of Uncertainty," IEEE Trans. Instrum. Measu., 58 639-648 (2009).