Correlation: An overlooked oscilloscope measurement

June 22, 2015 // By Arthur Pini
The correlation function is a useful signal-analysis tool that engineers often overlook. Its formidable equation, which you have probably not thought about since your undergraduate signals and systems course, is.....

where f1 and f2 are real functions of time (t) and τ represents a delay.

You can forget the pain that this equation evoked in your earlier life because modern oscilloscopes and third-party math software easily perform all the computations and make this powerful function available to everyone. Correlation can be classified into either of two functions, auto-correlation or cross-correlation, depending on the number of inputs. In this article, we'll show some common applications for both cross-correlation and auto-correlation.

Correlation functions

Correlation functions were added to the available math functions in oscilloscopes to support two optional diss drive measurements, ACSN (auto-correlation signal to noise ratio) and NLST (non-linear transition shift). While these measurements may not be of general interest, their presence makes the correlation function available for more general applications.

Auto-correlation is the correlation of a signal with itself (single waveform). It provides a measure of the similarity between observations as a function of the time lag between them. It is an analysis tool for finding repeating patterns, such as the presence of a periodic signal buried in noise.

Cross-correlation measures of the similarity of two waveforms as a function of a time delay between them. Cross-correlation is used to search for a known short signal in a longer signal (detection) or to measure a time delay between two signals with a common source.

Auto-correlation example

Auto-correlation is typically used to detect periodicity within a signal. In Figure 1, the top grid (channel 1) contains the input signal. It is a 10 Mbps, NRZ (non-return-to zero) PRBS (pseudorandom bit stream) with a PRBS7 pattern that repeats every 127 clocks. It is pretty obvious that there is a repetitive pattern. The next grid down contains the auto-correlation of that PRBS7 signal.

Figure 1. The auto-correlation of a PRBS7 in the upper trace shows the waveform with good SNR. The second trace from the top is the auto-correlation function showing peaks spaced