Sparsity Problem Involving Rational Basis Functions

In this paper we consider the problem of sparse signal modeling by means of rational functions. Our dictionary is composed by a finite collection of elementary rational functions. In order to represent the signal with minimal error, we select an optimal number of basis from this set. The mutual coherence is a fundamental attribute of the dictionary. We analyze this quantity and describe its relation to the free parameters, i.e., the inverse poles, of rational functions. Then, we demonstrate the efficiency of sparse rational representations by compressing real electrocardiograms (ECG) including comparisons with other methods.