Calculating non-equidistant discretizations generated by Blaschke products

The argument functions of Blaschke products provide a very elegant way of handling non-uniformity of discretizations. In this paper we analyse the efficiency of numerical methods as the bisection method and Newton's method in the case of calculating non-equidistant discretizations generated by Blaschke products. By taking advantage of the strictly increasing property of argument functions we may calculate the discrete points in an enhanced order — to be introduced here. The efficiency of the discrete points' sequential calculation in this order is significantly increased compared to the naive implementation. In our research we are primarily motivated by ECG curves which usually have alternating regions of high or low variability, and therefore different degree of discretization is needed at different regions of the signals

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. Includingin 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. <br /