dc.description.abstract | Operator theory concepts such as frame operator, Gramian operator, synthesis operator and analysis operator
are useful in signal processing and telecommunication. Finite dimensional Hilbert spaces and normalized
(unit) vectors are rich in signals required in application. One of the most significant fields of applications
and source of questions of group theory and operator theory is frames. The Mercedes- Benz frames are
highly applicable in signal processing. In this thesis; we investigate frames, fourier analysis and wavelets and
some of their applications in signal processing and telecommunication. We investigate why we need frames
over bases, we study the dual frames, some operators: synthesis, analysis, frame and Gramian and finalize
frames by looking at group frames. Here, we shall investigate the relationship between group symmetry and
frames, representation theory and frames and also study group matrices and the Gramian of a group frame.
We shall investigate properties of fourier analysis. We finalize by looking at the applications of frames and
wavelets in signal processing and telecommunication. | |