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Time Is On Your Side: An Overlooked Averaging Type, Part 1

Blog Post created by benz on Sep 15, 2016

Originally posted May 1, 2014

Get a quick SNR improvement of 10 to 20 dB—when the conditions are right

The topic of averaging comes up a lot in RF measurements and in this blog. I suppose it’s an unavoidable consequence of the fact that the universe is noisy and we engineers are striving instead for a quiet certainty.

Most discussions of averaging focus on smoothing data to reduce the effect of noise and therefore the variance of measurement results. As described previously, it’s important to reduce variance efficiently and without distorting the results.

However, as explained last time, the right type of averaging can modestly improve the signal/noise ratio for certain measurements instead of simply smoothing them. This is a very fortunate situation, albeit limited to CW signals near noise.

Another fortunate situation, and one with a bigger benefit, revolves around signals that repeat consistently. Such signals are common in communications, navigation and imaging, all applications in which improved dynamic range—not just reduced variance—is valuable.

These repeating signals represent additional information, giving us the chance to go beyond the well-known good/fast/cheap tradeoffs.

Information is the third element in this useful triad of measurement tradeoffs. The diagram symbolizes how measurements may be improved by treating information as an input to improve the measurement process and not merely an output.

Information is the third element in this useful triad of measurement tradeoffs. The diagram symbolizes how measurements may be improved by treating information as an input to improve the measurement process and not merely an output.

Just as it’s easy—for me, at least—to underestimate the magnitude of noise, it’s also easy to underestimate the additional information represented by repeating signals. So how do we harness this information to make better measurements?

The answer is time averaging, also referred to as synchronous or vector averaging. As the names imply, this type of averaging operates in the time domain and accounts for magnitude and phase or I and Q, as shown in the figure below.

The time averaging process is shown graphically for repeated samples of a single point in a repeating signal. Vector averaging of the samples quickly converges on a better measurement (red dot) of the signal’s actual value.

The time averaging process is shown graphically for repeated samples of a single point in a repeating signal. Vector averaging of the samples quickly converges on a better measurement (red dot) of the signal’s actual value.

The concept is straightforward: A repeating signal is sampled on a time scale precisely synchronized with its repetition interval, and the analyzer’s RF downconversion is phase-stable with respect to the signal. Samples from each repetition of the signal are averaged in I/Q or magnitude/phase to form a time record for any type of analysis, including time, frequency and demodulation. Noise is uncorrelated with the signal and is averaged out, as shown above.

The fundamental thing to understand about time averaging is the noise is not smoothed and the variance may not be reduced. Instead, most of the noise is effectively removed. That’s the magic of adding information to the measurement!

When seen in operation, it does look a little like magic. In many cases, hundreds of averages can be performed in a second or two, and the measurement noise floor plunges by 10 to 20 dB!

The other part of the magic is that the improvement in dynamic range applies to all kinds of measurements in the time, frequency and modulation domains.

This averaging type is available standalone on Agilent’s X-Series signal analyzers and the PSA spectrum analyzer, and on other measurement platforms through the 89600 VSA software.

In the next post I’ll illustrate the benefits of time averaging using an example or two, and discuss some practical implementations and limitations. This averaging won’t suit every situation, but it’s a powerful way to make the best use of in-hand information and produce better measurements.

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