Autocorrelation

Correlation describes how two functions compare when one is delayed in time. If the two functions are the same function, it is called autocorrelation. Obviously a function will correlate with itself perfectly with zero delay. If the function is a sinusoid, it will also correlate perfectly when one is delayed by the period T (correlation =1). When it is delayed by T/2, correlation = -1. In general, it will be a sinusoidal function of delay.

One use for autocorrelation is to detect multipath interference in a received signal, where the signal will be the sum of multiple copies with different amplitudes and delays. Once the delays and amplitudes of the interference is determined using autocorrelation, this interference can be removed with the appropriate signal processing.

When calculating DIGITAL autocorrelation, all points in each waveform are added for both functions, first with no offset (lag value), then the two are summed to get one number. Then one lag value is used (a delay of one sample) to get the second value (it will always be lower for ACf). these lag values are continued until the entire sample is finished. For a sine wave, the ACf waveform will now be a cosine wave, since max value is at zero lag.

A problem known as "wrap-around error" is avoided by padding the two wave forms with an equal number of zeros. This will produce a diminishing ramp for the final waveform, which can be compensated for with a final block math addition.