Korrelatoren

Korrelatoren are devices or algorithms used to measure the degree of correlation between signals or datasets, or to determine correlation functions of stochastic processes. They can be implemented as hardware modules, software programs, or a combination of both, and are used in a wide range of disciplines.

In signal processing, the two primary forms are the cross-correlation between two signals and the autocorrelation of a single signal. For continuous signals, the cross-correlation is defined as Rxy(τ) = ∫ x(t) y(t+τ) dt, and for discrete signals as Rxy[k] = Σn x[n] y[n+k]. Autocorrelation is the special case where y = x. Normalization gives a correlation coefficient that ranges between -1 and 1, aiding comparison across signals with different scales.

Hardware correlators accumulate products of input samples over time, while digital correlators rely on software or digital signal processors. Modern digital implementations often use the FFT to compute cross-correlation efficiently, leveraging the convolution theorem: cross-correlation equals the inverse FFT of the product of the FFTs of the signals.

Applications span timing and synchronization in communications, radar and sonar, delay estimation, and pattern recognition. In astronomy, correlators are used in interferometry to combine signals from multiple telescopes. In time-series analysis and neuroscience, correlation measures help identify relationships and dependencies between signals.

See also: cross-correlation, autocorrelation, convolution, Fourier transform, synchronization.