Time-Frequency Representations

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Focusing on the intersection of time-frequency analysis and abelian group theory, this work emphasizes the unifying role of group structures in developing theory and algorithms. It is divided into two parts: one covering Weyl-Heisenberg representations over finite abelian groups, and the other addressing multirate filter structures over free abelian groups of finite rank. The methods employed are dimensionless and coordinate-free, facilitating applications to both one and multidimensional problems, while prioritizing simplicity over mathematical necessity.