A Study Of M-band Periodic Wavelet Frames Using Extension Principles

Since the extension principles of constructing wavelet frame were presented, the researches around this direction was gradually started, especially when the extension principles were applied to the period wavelet frame, there were already many researches of extension principles of periodic wavelet frames. However,nowadays most of the study of periodic wavelet frames are on 2-band. With the development of wavelet, it has many limits in application. In this paper, we first review the M-band unitary extension principle and the M-band mixed extension principle, and give a corollary of M-band mixed extension principle——the mixed oblique extension principle, then prove that the mixed extension principle and mixed oblique extension principle is equivalent to make it easier to understand the real significance of the dual frame. Next we extend the periodic wavelet frames to the M-band with unitary extension principle and mixed extension principle, on this basis, we get the constructions of M-band periodic wavelet frames, and provide a theoretical guide in the practical application of wavelet frame.