Truncation based model order reduction techniques and their application to digital audio filters

Abstract

Model order reduction aims to reduce the order of high-order dynamical systems while preserving most of their input-output behaviour. In this thesis, we will give a short introduction to model order reduction and examine two methods in detail that are considered truncation techniques, balanced truncation and modal truncation. We will discuss some of their properties and apply these methods to a real-life scenario by trying to reduce the order of several digital audio filters. These filters are models that process a digital audio signal to generate varying sounds. Next, we will compare the results of different reductions in terms of a computable error bound on the approximations. We will see that for our specific type of filter, balanced truncation seems to be able to provide the best reductions, where we can sometimes find an accurate approximation with an order reduced by more than 50%.