Visualizing Probability Density of Time-Stamped Measurements

The availability of precision time synchronization, such as that provided by IEEE 1588 Precision Time Protocol, make it desirable to have signal processing methods available for signals sampled at non-uniform intervals but but with accurately recorded sample times, called time stamps. One common analysis tool for uniformly sampled measured data, the histogram, is used to visualize the probabilities of measured values occuring. When measurements are not uniformly sampled, however, the measured values cannot simply be binned into a histogram. A new method is presented for visualizing the probability density of a time-stamped, non-uniformly sampled signal. A bank of rank-order filters is used to produce a time-varying estimate of the cumulative density function of the signal. The approximate derivative of that function estimates the probability density function of the signal. An example is presented of use of the proposed method on actual measured data.