Fast cross-correlation algorithm with application to spectral analysis

A method for transfer function calculation is described that derives its economy from the symmetry of the autocorrelation to double the number of lags. The imbalance in the number of lags between autocorrelations and cross-correlations is restored by calculating the negative lags of the cross-correlation without any extra computations. With both positive and negative lags available, the symmetry and periodicity constraints of the fast Fourier transform can be taken into account, and windowing the cross-correlation sequence is less ambiguous. This greatly increases the accuracy and convergence of the computed transfer function. Since the statistical significance of the transfer function estimate is higher, it is possible to obtain the transfer function using shorter data sequences. These last advantages more than outweigh the increase in resolution