Research On Minimum-Energy Wavelet Frame On The Interval And Its Application In Signal Denoising

Frame theory is one of efficient tools in the signal processing. At present frame theories have been widely used in wavelet analysis, image processing, numerical analysis, etc. In this paper, we first elaborates on the basic principles of frames and wavelet transforms, and constructs a class of minimum energy frames in L~2 [0,1], which not only allow the design more freedom, can have the properties in the applications with symmetry and (or) anti-symmetry, compact supports, good time–frequency localized representations and shift-invariance, but also can solve the un-matching between the space of L~2 (R) and the signal space of L~2 (K) . And then, we obtain the necessary and sufficient conditions of the minimum energy frames in L~2 [0,1]. In the final, we give the decomposition algorithm.The results of the experiments indicate that the frames constructed by us are more useful than the orthonormal wavelets in the application of signal de-noising.