Time-Frequency Representations

Focusing on time-frequency analysis through the lens of abelian group theory, this work highlights the unifying role of group structures in developing theory and algorithms. It is divided into two parts: the first explores Weyl-Heisenberg representations on finite abelian groups, while the second addresses multirate filter structures on free abelian groups of finite rank. The methods used are dimensionless and coordinate-free, making them applicable to both one and multidimensional problems. The selection of topics prioritizes simplicity to facilitate immediate application in algorithm design for time-frequency processing.