Signal Decomposition Into Primitive Known Signal Classes
David G. Galati · D-Scholarship@Pitt (University of Pittsburgh) · 2002
The detection of simple patterns such as impulses, steps, and ramps in signals is a very important problem in many signal processing applications. The human eye is a very effective filter and hence is capable of performing this task very efficiently. In applications where no humans are involved in the signal interpretation process, this task needs to be performed by a computer. In this thesis, we propose and investigate two novel algorithms to automate this task. Our starting point is a discrete signal composed of an unknown number of ramps, steps, and impulses with unknown magnitudes and delays as well as random noise. We propose two different criteria based on "minimum energy" and "minimum complexity" to decompose the signal into these basic simple patterns. The solutions based on these criteria are proposed and examined. Over all, the "minimum complexity" criterion seems to produce results that are more similar to the human eye's interpretation then the "minimum energy" approach.