On Analysis and Synthesis Operators and Characterization of Synthesis Matrix of a Frame in Terms of Frame Operator
Keywords:Frame, analysis, synthesis, adjoint, Gramian, dual, operators
In this research paper we introduce the operators associated with a frame. That is the Analysis and the Synthesis Operators and their basic properties. The structure of matrix representation of the Synthesis operator is also analysed. This matrix is what most frame constructions in fact focus on. The frame operator which is just the joining together of the analysis and synthesis operators is fundamental for the reconstruction of signals form frame coefficients. We also give a complete characterization of the synthesis matrix in terms of the frame operator.
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