Spectral Techniques: The First Decade of the XXI Century (Invited Paper)

Following an “unwritten tradition” this paper offers a review of another decade of achievements in the area of Spectral Techniques. Topics like transforms of matrix-valued functions, transforms based on non-Abelian groups, latest advancements related to Linear Independent transforms, a space-efficient algorithm to calculate spectral transforms, will be discussed. A special mention will be given to other areas, like signal processing, and coding theory, where Spectral Techniques have been (and continue to be) used, even though with possibly different names.