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 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 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