Open AccessOn Analysis and Synthesis Operators and Characterization of Synthesis Matrix of a Frame in Terms of Frame Operator
Author(s) -
Loyford Njagi,
BM Nzimbi,
S.K Moindi
Publication year - 2018
Publication title -
journal of advance research in mathematics and statistics
Language(s) - English
Resource type - Journals
ISSN - 2208-2409
DOI - 10.53555/nnms.v5i12.524
Subject(s) - frame (networking) , operator (biology) , algebra over a field , matrix (chemical analysis) , characterization (materials science) , operator theory , mathematics , matrix representation , representation (politics) , computer science , pure mathematics , physics , telecommunications , group (periodic table) , biochemistry , chemistry , materials science , repressor , quantum mechanics , politics , transcription factor , law , optics , political science , composite material , gene
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.