Interrelations among the spectral expressions of the information measures of Kullback-Leibler (1959) and Renyi (1961) for discrimination between two stationary Gaussian time series are discussed. The spectral expression of Fisher's information rate matrix is also treated, as well as two intuitively acceptable discrimination functions. It is shown that all of them are equivalent except for scalar multiplication and are expressed by Fisher's information rate matrix in the sense of their second-order Taylor series approximation. Finally, a relation between two criteria for order determination of models for time series data, namely, H. Akaike's (1974) information criterion (AIC) and the criterion of autoregressive transfer functions (CAT), is discussed in connection with these spectral expressions.>

Identification and recursive filtering problems related to a signal described by a Markov chain plus autoregressive(MCPAR) process are considered. These subjects are motivated by application to modelling of 1-D image data with multipeaks in their histgram of gray levels as well as by describing some real data such as ones measured from random nonlinear vibration etc.. Firstly both recursive and iterative identification algorithms are presented based upon the minimum prediction error method. Secondly a new suboptimal algorithm of the minimum mean square estimate of the MCPAR signal from noisy corrupted data is proposed. Finally computer simulation results for our proposed algorithms are contained.