A Study Of M-band Minimum-energy Frames On The Interval

From the wavelet multiscale analysis angle, the constructions of M-band interval minimum-energy wavelet frames are studied in this paper. We give the definition of M-band interval minimum-energy wavelet frames, and give the necessary and sufficient conditions for the M-band minimum-energy frames for L2 [0,1]; from the interval multiresolution analysis angle, by the cut-back method, we give the ways to modify existing scaling functions in the space of L2(R) to construct M-band interval frame scaling function on L2[0,1], and also give the theorem of M-band interval frame wavelets function corresponding to M-band interval frame scaling function; firstly give the theorem of M-band minimum-energy frames with arbitrary integer supportγon L2[0,1]; finally we provide the decomposition and reconstruction formulas of M-band interval minimum-energy wavelet frames; some examples are given at last.