Covariance sequence approximation for recursive digital filter design

In this paper we explore an alternative solution to the general nonlinear least squares approximation problem for digital filter design. We choose to approximate covariance sequences because they arise more naturally than unit pulse sequences when approximating spectra and when identifying ARMA sequences from random data. The design procedure resulting from this approach requires solution of a nonlinear algebraic equation in the form of a polynomial rootfinding problem, in addition to solving a system of linear equations and an Inverse Discrete Fourier Transform (IDFT).