On the equivalence of z-domain and s-domain: The inverse of convolution integral and its application to systems identification

In this work we present an equation that obtains the Laplace transform of a time function from its z-transform. This equation is the integral representation of the inversion of the well know convolution integral, which obtains the z-transform using the Laplace transform. The paper also presents the application of the presented method to obtain the estimation of continuous systems through their discrete time samples.