An efficient algorithm for computing the triple correlation

The triple correlation C[k,m] is of the class of higher-order statistics and is used in a number of signal processing applications. Its computational requirements are of the order of K.M.N (the maximum lags and the number of data points respectively) and in any practical situation this amounts to a significant burden. The algorithm we present in this paper exploits the redundancy of the product terms to derive a factored expression for C[k,m] that results in a reduced number of multiplications (and overall operations). The savings depend on the relationships between the 2 lags and the number of data samples. Details for each case are provided and numerical examples illustrate the algorithm's effectiveness.