Volume of the space of finite autocorrelations

A method is developed for computing the volume of the space occupied by valid finite autocorrelation sequences of any order p . The method is based on transforming an integral over autocorrelations to an integral over the lattice coefficients of an all-zero filter to order p. The resulting integral was compared numerically using a Monte Carlo method and an importance sampling technique that helped concentrate the sample values where much of the volume is. Good accuracy for the volume estimate was obtained up to p=50. The results show that the space occupied by finite autocorrelations is roughly one-half that occupied by all positive definite autocorrelations along each of the p dimensions