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.<
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