NOTE ON COVARIANCE-INVARIANT DIGITAL-FILTER DESIGN AND AUTOREGRESSIVE MOVING AVERAGE SPECTRUM ANALYSIS

Consider an autoregressive-moving average (ARMA) discrete-time sequence {xk} with covariance sequence {Rk}. Equations are given for the solution of the AR coefficients {ak}n1 in terms of the covariances {Rk}2n−10 and subsequent solution for the MA coefficients {bk}n1 in terms of the AR coefficients and the covariances {Rk}n−10. The results are derived and presented somewhat differently than usual to complement the results of [1] for the synthesis of covarianceinvariant digital filters. In the context of spectrum analysis, the results provide a means of performing ARMA spectrum analysis on data that arise as sampled data from a rational continuous-time process [2]. An important result, originally derived in [2], shows that the ARMA spectrum can be obtained without actually solving the nonlinear factorization problem for the MA coefficients. © 1979 IEEE