Just the FAQs: Waveform Averaging

Figure 1: The upper grid displays raw samples directly from
the ADC; the lower grid displays the average of 1000
acquisitions.

If you've poked around the Teledyne LeCroy website, perhaps you've run across the extensive (and growing) collection of test-related tidbits we call our FAQ Knowledgebase. To highlight some of these helpful hints for making better use of your oscilloscopes, protocol analyzers, network analyzers, etc., we'll post some here on the Test Happens blog from time to time.

When we input a signal to our oscilloscopes, we generally find that there are two main components to what leaves the data acquisition front end and is the subject of subsequent processing, analysis, and characterization: the signal of interest and some amount of noise.

Most of that noise comes from the data acquisition front end's wideband amplifier, increasing with the square root of the bandwidth. The last thing you want is to spend time analyzing the quality of your signal source only to learn that you'd really been characterizing noise that was added in the acquisition process.

There are a few solutions to the problem of characterizing signals in the presence of noise. One is to start with a low-noise, high-resolution oscilloscope such as Teledyne LeCroy's HDO and HRO 12-bit oscilloscopes. Doing so largely alleviates the noise issue from the start thanks to the instruments' extremely low-noise front ends and signal paths.

However, in the absence of a 12-bit data-acquisition front end, there are other ways in which oscilloscope makers seek to mitigate the corruption of acquired signals with wideband amplifier noise. A common means is waveform averaging (Figure 1). The user sets up a trigger and compiles a large numbers of acquisitions. A math buffer adds up N acquisitions and divides by N to reduce the noise level. With this technique, the oscilloscope can display the most recent acquisition (with the attendant noise) as well as the averaged signal to display the effect of the averaging.

It should be noted that waveform averaging has its limitations. First, the signal of interest must be repetitive in nature; waveform averaging is not applicable to signals that are unstable or plagued with intermittent glitches. Second, the signal feature of interest for viewing and/or measuring must be stable in time with respect to the trigger event that initiates waveform captures. Third, the property being measured should be unrelated to signal quality, because the averaging process dramatically changes the quality of the signal by removing noise—both the acquisition noise of the instrument's front end and the true noise that is actually part of the signal. Thus, measurements of signal quality such as signal-to-noise ratio, eye patterns, and jitter should steer clear of waveform averaging techniques.

Two broad categories of waveform averaging are summed averaging and continuous averaging. The former is the repeated addition, with equal weight, of successive source waveform records. With a stable trigger available, the resulting average has a random noise component lower than that of a single-shot capture. Upon reaching the maximum number of sweeps, the averaging process stops.

Continuous averaging, which is the default mode for Teledyne LeCroy oscilloscopes, is the repeated addition, albeit with unequal weight, of successive source waveforms. This approach is particularly useful for reducing noise on signals that drift very slowly in time or amplitude. The most recently acquired waveform has more weight than all of the previously acquired ones. Thus, the statistical fluctuations of the most-recently acquired waveform dominates the continuous average. The weight of earlier acquisitions in the continuous average gradually tends to zero (following an exponential rule) that decreases as the weight increases.