Theoretical Analysis of Cross-Correlation of Time-Series Signals Computed by a Time-Delayed Hebbian Associative Learning Neural Network

A theoretical proof of the computational function performed by a time-delayed neural network implementing a Hebbian associative learning-rule is shown to compute the equivalent of cross-correlation of time-series functions, show- ing the relationship between correlation coefficients and connection-weights. The values of the computed correlation coef- ficients can be retrieved from the connection-weights.