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Revisiting the history of jitter: Histograms

25 May 2015  | David Maliniak

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Continuing our review of the history of jitter and the evolving response to it, we'd arrived at the late 1990s, when more sophisticated analysis methods were necessary to get a good handle on jitter. In particular, statistical analysis came onto the scene. Statistics are a great tool for analyzing phenomena such as jitter that change more as you look at them harder.

A simple, yet telling, application of statistical analysis to the characterization of jitter is to use histograms to compile a statistical distribution of edge arrival times (figure 1). However, if we were to look at four different signals, we would see four different distributions. But those distributions all have at least one thing in common. If you look at the outside edges of each of the histograms, they all exhibit a similar shape. There's a "falling-off" shape to those edges that's half-Gaussian, or random, in character.

Figure 1: An example of using histograms to plot the statistical distribution of edge arrival times.

Consider the histogram at the upper left of figure 2 (or any of them, for that matter). What it reveals is that jitter has two broad components. Keep in mind what a histogram is: It shows us the shape of the statistical distribution of parameter values. So when we look at that upper-left display, what we see is that jitter has two parts. Those "falling-off" Gaussian tails at either end of the distribution, shown in white, represent the random component of jitter. This component of jitter is unbounded, so statistically speaking, the longer you measure, the larger it gets, because theoretically, an edge can arrive anywhere at any time.

Figure 2: Jitter has two main components: random (in white in all four histograms) and deterministic (in salmon).

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