An optimal method for identification of pole-zero transfer functions

An optimal algorithm for estimation of the parameters of rational transfer functions from prescribed impulse response data is presented. The proposed method is based on the minimization of the l₂ -norm of the true fitting error and is uniformly applicable for rational models with arbitrary numbers of poles and zeros. Existing methods either modify the true nonlinear error criterion in the theoretical derivation or require the transfer function model to have exactly one less number of zeros than poles. The multidimensional nonlinear error criterion is decoupled into a purely linear and a nonlinear subproblem of reduced dimension. The inherent mathematical structure in the non-linear subproblem is exploited in formulating an efficient iterative computational algorithm for its minimization. The effectiveness of the algorithm is demonstrated with several simulation examples