A Class Of Periodic Wavelets And Their Application

In his monograph: An Introduction to Wavelets Through Linear Algebra, Frazier constructs the D₆ wavelet in l²(Z_N), by using the method of frequence domain. In this thesis, we give a family of orthogonal wavelets with only six nonzero coordinates in l²(Z_N), by using the method of time domain, which include the D₆ wavelet. The effects are compared, when the tensor products of these wavelets are applied to the blur image compression and the threshold compression.The thesis is organized as follows: in the first chapter, some related notations, definitions, the background and the main results are given; in the second part, we discuss the construction of Dq type wavelets and their applications in the case of one dimension, as well as the interpolating and symmetric properties; in the third one, we apply D₆ type wavelets of l²(Z_N1 × Z_N2) to image compressions.