Fitting a pole-zero filter model to arbitrary frequency response samples

The authors propose a method to fit a discrete-time pole-zero filter model H(z)=A(z)/B( z) to arbitrary complex-valued frequency response samples Y (u_i), i=0, 1, . . ., t in the least-square sense. An important attribute of the technique is that the frequency locations u_i, i=0, 1, 2, . . ., t need not be equally spaced around the unit circle. The initial estimates of the denominator coefficients of the model system function H(z) are obtained by using an iterative algorithm. Starting from these initial estimates, a Newton-Raphson gradient technique is used to reach a minimum of the error criterion. The numerator polynomial coefficients are subsequently obtained by solving another set of linear equations. Simulation results using a filter design example are provided