ON ANALYSIS AND SYNTHESIS OPERATORS AND CHARACTERIZATION OF SYNTHESIS MATRIX OF A FRAME IN TERMS OF FRAME OPERATOR.
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.
Comput. Harmon. (2007)
2. Bodmann, B., Casazza, P.G.: The road to equal-norm Parseval frames. J. Funct. (2010)
3. Bodmann, B.G., Casazza, P.G., Kutyniok, G.: A quantitative notion of redundancy for finite
frames. Appl. Comput. Harmon. (2011)
4. Bodmann, B.G., Casazza, P.G., Paulsen, V.I., Speegle, D.: Spanning and independence properties
of frame partitions. Proc. Am. Math. Soc. (2012)
5. Bodmann, B., Lipshitz, S.: Randomly dithered quantization and sigma-delta noise shaping
for finite frames. Appl. Comput. Harmon. (2008)
6. Bodmann, B.G., Paulsen, V.I.: Frames, graphs and erasures. Linear Algebra Appl. (2005)
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