An improved algorithm for high speed autocorrelation with applications to spectral estimation

A common application of the method of high speed convolution and correlation is the computation of autocorrelation functions, most commonly used in the estimation of power spectra. In this case the number of lags for which the autocorrelation function must be computed is small compared to the length of the data sequence available. The classic paper by Stockham, revealing the method of high speed convolution and correlation, also discloses a number of improvements in the method for the case where only a small number of lag values are desired, and for the case where a data sequence is extremely long. In this paper, the special case of autocorrelation is further examined. An important simplification is noted, based on the linearity of the discrete Fourier transform, and the circular shifting properties of discrete Fourier transforms. The techniques disclosed here should be especially important in real-time estimation of power spectra, in instances where the data sequence is essentially unterminated.