A new insight into Wavelet Transforms using the concepts of Frame Theory

Abstract

Wavelet analysis being a relatively new subject of study is being explored, all around the globe, using various mathematical tools, currently available. This paper is a humble attempt to provide a comprehensive study of the same, by means of exhaustive mathematical analysis. Since frame theory has been established as a standard notion in applied mathematics, so it was used as the analytical tool to explain the formation, purpose and use of wavelets. The theoretical explanation follows the mathematical analysis, which is an attempt to give picture the ‘theorems’, ‘definitions’ and the ‘lemmas’.