Yoshimi Monden

Fast algorithm for identification of an ARX model and its order determination

In this paper, we present a fast algorithm for fitting ARX models and determining their orders from the covariance and cross-covariance information of input and output processes. Ascending and descending order-update recurrences will be presented first for fitting an ARX model. These recurrences will be applied to the order determination of ARX models based on Akaikes information criterion. This algorithm reduces the computation required for fitting an ARX model (m, n) and its associated order determination to a number of operations proportional to 0[ (m + n)2], compared to the usual Cholesky decomposition method which requires a number of operations proportional to 0[(m + n)4]. Some numerical examples, as well as the Pascal source programs, are presented to illustrate the efficiency of this algorithm.

The continuous-time limit of the discrete-time stability theory

This paper elucidates the correspondence between the Schur-Cohn (SC) test and the Routh-Hurwitz (RH) test by showing that the latter is obtained as a limit of the former. The argument is developed in a stochastic framework, where stochastic interpretations of the tests are used. The interpretation of the SC test can be derived from its equivalency to the Levinson-Durbin algorithm, while that of the RH test is newly presented here.

Statistical design of nearly linear-phase ARMA filters

This paper proposes a method for statistical design of approximately linear-phase autoregressive-moving average (ARMA) digital filters. The key idea of our method is that a time-delayed ARMA filter is used to approximate a high-order FIR filter that meets the prescribed amplitude spectrum sufficiently well. Computer simulations show that the resulting ARMA low-pass, bandpass, and high-pass filters not only meet the prescribed amplitude response specification well, but yield excellent linear phase with much lower order and smaller delay compared to the associated FIR filters.