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.
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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 disk 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, like 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.