(The) minimal degree polynomial oblique dual generators of the Riesz sequences of B-spline shifts

Abstract

In the field of signal processing, the concept of the dual basis is important in decomposing an analog signal into discrete representation. In the recent, study of the compactly supported oblique dual generators associated to the Riesz sequences of integer-shifts is done by Christensen et al. In this thesis, we study the polynomial oblique dual generators of the Riesz sequences of integer translates which has the minimal degree. We present an algorithm to find a minimal degree polynomial oblique dual generator of the general Riesz sequences of the integer shifts. In addition, we show that the minimal degree of a polynomial oblique dual generator associated to B-spline of order N is N-1. Furthermore, we present two conjectures about the properties of the compactly supported polynomial oblique dual generators such that we have found during this research.