Statistical design of ARMA filters

Procedures are given for the systematic design of ARMA filters. All of the design algorithms are linear and of the Levinson type. Each design is initiated with a long AR approximation of an ideal spectrum. The long AR is used to generate consistent unit pulse and covariance sequences for use in the Levinson type algorithm of Mullis and Roberts. The latter algorithm allows one to approximate the unit pulse and covariance sequences and thereby obtain a low-order ARMA approximation. There is no need for the ARMA approximation to be proper.