A comparative study of wavelets and multiwavelets.

Abstract

In this thesis, some basic concepts and theorems are studied, leading to the cascade algorithm which is the most usual approximating method used in the construction of wavelets. By considering the symmetry property of scalar wavelets, Lawton's complex-valued scalar wavelets are studied and some recent results are implemented in the theory of complex-valued scalar wavelets. Another important part of this thesis is the study of multiwavelets. Some comparisons are made among real-valued scalar wavelets, complex-valued scalar wavelets and real-valued multiwavelets. A special contribution is the figures of different kinds of wavelets and some numerical results.