#### Correlation

Correlation is a measure of the similarity between two waveforms. It is a method of time-domain analysis that is particularly useful for detecting periodic signals buried in noise, for establishing coherence between random signals, and for establishing the sources of signals and their transmission times.

In radar signal processing correlation means to compare an unknown signal against a known reference signal to determine
their similiarity as a function of the displacement of one relative to the other.
It is a function of the relative time between the signals, whose mathematical equation differs for analog and digital signals.

For analog signals it is the sum of the matching surfaces of the two waveforms:

For discrete or digital signals, the sum of matching sub-pulses:

…where the time shift τ or m is called the lag.

The reference signal is mostly “normalized”, or given to as an ideal model. The amplitude values of the correlation result are not fully normalized, i.e. maximal correlation will be less than 1. If the correlated unknown signal is identical with the reference, then the result of correlation is 1. This is an important special case, called autocorrelation. Autocorrelation can assist in detecting periodicities.

A practical implementation of a correlation is, for example, the matched filter, and the range measurement in Noise Radar.

Source:

- Jonathan Yaakov Stein: “Digital Signal Processing: A Computer Science Perspective”, Wiley-Interscience, 2000, ISBN 0-471-29546-9, p. 354