The Bivariate Minimum-Energy Tight Wavelet Frames and Applications in Economics and Management

Abstract

Material science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. Frames have become the focus of active research field, both in the-ory and in applications. In the article, the binary minimum-energy wavelet frames and frame multi-resolution resolution are introduced. A precise existence criterion for minimum-energy frames in terms of an ineqity condition on the Laurent poly-nomial symbols of the filter functions is provided. An explicit formula for designing minimum-energy frames is also established. The sufficient condi tion for the existence of tight wavelet frames is obtained by virtue of a generalized multiresolution analysis.