In this paper we want to describe some examples of the active interaction that takes place at the border of rational approximation theory and linear system theory. These examples are mainly taken from the period 1950-1999 and are described only at a skindeep level in the simplest possible (scalar) case. We give comments on generalizations of these problems and how they opened up new ranges of research that after a while lived their own lives. We also describe some open problems and future work that will probably continue for some years after 2000. Key words: Rational approximation, linear system theory, model reduction, identication. ? This work is partially supported by the Belgian Programme on Interuniversity Poles of Attraction, initiated by the Belgian State, Prime Minister's OÆce for Science, Technology and Culture. The scientic responsibility rests with the authors. 1 This work of this author is also partially supported by the Fund for Scientic Research (FWO), project \Orth...

Autoregressive (AR) modeling by linear prediction (LP) provides the basis of a wide variety of signal processing and communication systems including parametric spectral estimation and system identification. Perhaps the greatest success of linear prediction techniques is to be found in speech analysis and audio coding. In this paper, we first reviewed the general frameworks of predictive signal modeling and investigated various prediction filter structures including the modified linear predictor. We then empirically compared the compression performamce of these prediction filters by applying to the lossless audio compression system. We also applied different filter orders and block lengths for each filter to explore their influence on the compression ratio....