To Nreal random variables the sample autocorrelation coefficients, which are also theNFourier coefficients of a measure on the unit circle are associated. The polynomialsorthogonal with respect to this measure define the transfer functions of the Wiener-Levinsonpredictors. We show that the statistics of the zeros of those random polynomials exhibits auniversal law of crystallization on a circle of radius [1 - (lniV)/2n], nbeing the order of thepredictor. These results are supported by extensive computer experiments and backed by atheoretical scaling argument in the asymptotic domainInN«n«N.These results areindependent of the nature of the noise and robust for signals of finite lengthN.
ASJC Scopus subject areas
- Physics and Astronomy(all)