Characterizations of tight frame wavelets with special dilation matrices (Q624677)

Summary: We study all generalized low-pass filters and tight frame wavelets with special dilation matrix \(M\) (M-TFW), where \(M\) satisfies \(M^d = 2I_d\) and generates the checkerboard lattice. Firstly, we study the pseudoscaling function, generalized low-pass filters and multiresolution analysis tight frame wavelets with dilation matrix \(M\) (MRA M-TFW), and also give some important characterizations about them. Then, we characterize all M-TFW by showing precisely their corresponding dimension functions which are nonnegative integer valued. Finally, we also show that an M-TFW arises from our MRA construction if and only if the dimension of a particular linear space is either zero or one.