A new set of piecewise constant orthogonal functions for the analysis of linear SISO systems with sample-and-hold (Q1389053)

A new approach to the analysis of single-input single-output (SISO) systems working in a sample and hold (SH) mode is presented. First, an accurate analysis of already existing approaches is presented. The novelty of the point of view given here lies in: a) constructing orthogonal piecewise constant functions having analogies with the Haar functions and b) finding how to invert simple linear operators, like \((s+a)^{-1}\), without inverting any matrix. An analysis of the errors ocurring in using this (approximate) method is given. The approach given here is ingenious and allows to avoid lengthy computations related with the \(Z\)-transform. Some examples illustrate the validity of the proposed way.