The Characterization for Symmetric Tight Frames and Periodic Gabor Frames and Applications in Computer Engineering

摘要

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this paper, we discuss a new set of symmetric tight frame wave-lets with the associated filter banks outputs down sampled by several generators. The frames consist of several generators obtained from the low-pass filter using spectral factorization, with low-pass filter via a simple approach using Legendre polynomials. The filters are feasible to be designed and offer smooth scaling functions and frame wavelets. We shall give an example to demonstrste that so-me examples of symmetric tight wavelet frames with three compactly supported real-valued sym-metric generators will be presented to illustrate the results.