Please use this identifier to cite or link to this item:
Title: Wavelet frames of dilation factor M
Keywords: frame multiresolution analysis, fibres, wavelet frames
Issue Date: 13-Oct-2003
Citation: LIM ZHI YUAN (2003-10-13). Wavelet frames of dilation factor M. ScholarBank@NUS Repository.
Abstract: Based on a frame multiresolution analysis (FMRA) of dilation factor M, we establish quantitative criteria in the frequency domain for the construction of a tight wavelet frame generated by a minimum number of M-1 mother wavelets. We utilize the concept of fibres of closed shift-invariant subspaces in the frequency domain to show the existence of tight frames in the wavelet spaces and also to provide a method of constructing the mother wavelets. It is shown that M mother wavelets would always be sufficient to generate a tight wavelet frame. We also provide an alternative way of constructing the mother wavelets for the elementary case of M=2 based on the analysis of the Gramian. Finally, we extend our construction techniques to creating a sequence space FMRA which is related to periodic wavelet frames and show that the fibres of multiresolution subspaces in L2(R) also form a FMRA in l2(Z) and that the wavelets constructed for L2(R) can be used to construct wavelets for l2(Z).
Appears in Collections:Master's Theses (Open)

Show full item record
Files in This Item:
File Description SizeFormatAccess SettingsVersion 
multiframe.pdf416.23 kBAdobe PDF



Page view(s)

checked on Apr 20, 2019


checked on Apr 20, 2019

Google ScholarTM


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.