Title :
Spectrum estimation by interpolation of covariances and cepstrum parameters in an exponentional class of spectral densities
Author_Institution :
Dept. of Math., R. Inst. of Technol., Stockholm
Abstract :
Given output data of a stationary stochastic process estimates of the covariances and cepstrum parameters can be obtained. Methods of moments have been applied to these parameters for designing ARMA processes, and it has been shown that these two sets of parameters in fact form local coordinates for the set of ARMA processes, but that some combinations of cepstrum parameters and covariances cannot be matched exactly within this class of processes. Therefore, another class of processes is considered in this paper in order to be able to match any combination of covariances and cepstrum parameters. The main result is that a process with spectral density of the form Phi(z) = (exp{Sigma k = 0 mpk(zk + z-k)})/(Sigmak = 0 nqk( z k + z-k)/2) can always match given covariances and cepstrum parameters. This is proven using a fixed-point argument, and a non-linear least-squares problem is proposed for determining a solution
Keywords :
autoregressive moving average processes; covariance analysis; parameter estimation; ARMA processes; cepstrum parameter estimation; cepstrum parameters; covariance estimation; covariance interpolation; covariances; nonlinear least-squares problem; spectral densities; spectrum estimation; stationary stochastic process; Cepstrum; Entropy; Interpolation; Moment methods; Polynomials; Process design; Spectral analysis; Stochastic processes; Transfer functions; USA Councils;
Conference_Titel :
Decision and Control, 2006 45th IEEE Conference on
Conference_Location :
San Diego, CA
Print_ISBN :
1-4244-0171-2
DOI :
10.1109/CDC.2006.377793