SOME LOCAL AND GLOBAL ASPECTS OF MATHEMATICAL DIGITAL SIGNAL PROCESSING

Abstract

We propose to use L^p norm of a given digital signal to identify the location where the dramatic chang occurs. The theory is based on Sobolev type inequalities on one dimensional intervals. We also study curve motions based on differential equations. Curve motion equations are classified into two types: adaptive equation and non-adapative equations. examples of both types of equations are studied and the global existences for these equations are proved based on integral estimates.