Volume of the space of autocorrelation sequences
J. Makhoul · 2003
One measure of the additional constraints placed on autocorrelation sequences is the volume of the space they occupy. The ratio of that volume to the volume of the hypercube circumscribing autocorrelation space can be interpreted as the probability that a random sequence restricted to less than one in magnitude is in fact a valid autocorrelation sequence. The author derives a closed-form expression for the volume of the space of an autocorrelation sequence of any order. The derivation throws additional light on the spectral sensitivity of small variations in an autocorrelation sequence near the positive semidefinite boundary.>