RAIT: the Rational Approximation and Interpolation Toolbox for Matlab, with Experiments on ECG Signals

There is a wide range of applications of rational function systems. Including in system, control theories and signal processing. A special class of rational functions, the so-called Blaschke functions and the orthonormal Malmquist--Takenaka (MT) systems are effectively used for representing signals especially electrocardiograms. We present our project on a general Matlab library for rational function systems and their applications. It contains Blaschke functions, MT systems and biorthogonal systems. We implemented not only the continuous but the discrete versions as well, since in applications the latter one is needed. The complex and real interpretations are both available. We also built in methods for finding the poles automatically. Also, some interactive GUIs were implemented for visual demonstration that help the users in understanding the roles of certain parameters such as poles, multiplicity etc.