#### Correlation

Correlation is a comparison between two waveforms and the measurement of the agreement. It is a time-domain analysis methodology that is particularly used in detecting periodic signals hidden in the noise, determining coherence between random signals, and determining signal sources and their transmission times.

In radar signal processing, correlation is understood as the comparison between an unknown signal and a known reference signal, or more precisely: their degree of coincidence as a time shift function between these two signals. It is a function of the propagation time between the signals whose mathematical equation is different for analog and digital signals. For analog signals, it is a function of time of the sum of the matching areas of the two waveforms:

For discrete or digital signals, it is a time function of the number of corresponding partial pulses:

…where τ or m is the respective time difference or delay (lag).

The reference signal is usually “normalized”, i.e. the conditions of origin are standardized or even based on an ideal mathematical model. The amplitudes of the result, on the other hand, are not standardized, i.e. the maximum agreement is less than 1. If the shape of the signal to be compared is identical to the reference, this is called autocorrelation. This special case can be used to detect periodicities in a mixture of signals.

A practical application of correlation is, for example, the matched filter as well as the method of distance measurement in a noise Radar.

Source:

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