ARMA-based time-signature estimator for analyzing resonant structures by the FDTD method

We propose an algorithm for estimation of the optimal "system" parameters of time sequences (TSs) computed by the finite-difference time-domain (FDTD) method, with the goal of accurate representation of the time-signature using low-order models. The FDTD method requires computation of very long time sequences to accurately characterize the slowly decaying transient behavior of resonant structures. Therefore, it becomes critical to investigate methods of reducing the computational time for such objects. Several researchers have argued that the FDTD-TS can be modeled as the impulse response (IR) of an autoregressive moving average (ARMA) transfer function. However, it is known that determination of ARMA parameters by IR matching is a complex nonlinear optimization problem. Hence, many existing methods in EM literature tend to use Prony-based, linear predictor-type spectrum estimation algorithms, which minimize a linearized "equation error" criterion that approximates the true nonlinear model-fitting error criterion. As a result, significantly high model orders are needed by these methods to achieve good corroboration in the frequency domain, especially when a magnitude spectrum has deep nulls or notches. We propose to use a deterministic ARMA approach, which minimizes the true nonlinear criterion iteratively, and attains significantly improved IR fit over Prony's (1795) method using fewer ARMA model parameters. For a given time-sequence of an analyzed circuit, the issues of model order selection and choice of decimation factor are also addressed systematically. The improved performance of the proposed algorithm is demonstrated with transient simulation and signal analysis of microstrip structures which manifest deep nulls in the frequency domain.