A multiple model and Pade approximation

Dali Zhang, Michael P. Lamoureux, Gary F. Margrave

The paper considers rational Pade approximation of the Z -transform function of a timedependent minimum phase signal. We present a derivation of reflection and transmission coefficients in layered media which are related to infinite impulse response (IIR) filters as a rational function of a special form. The rational ([p, q ]-Pade) approximation of the Z transform function is formulated as a constrained least squares minimization problem with regularization constraints provided by the minimum phase signal. Numerical simulations for reconstruction of the Z-transform function and its use as an inverse filter for a multiple model demonstrate the effectiveness of the presented approach.