A classification of the harmonic frames up to unitary equivalence

DOI10.1016/j.acha.2010.09.001zbMath1211.42028arXiv1312.5393OpenAlexW1978215724MaRDI QIDQ533497

Tuan-Yow Chien, Shayne F. D. Waldron

Publication date: 3 May 2011

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.5393

zbMATH Keywords

tight framesroots of unitysignal processingfinite abelian groupscharacter theoryPontryagin dualitygeometrically uniform framesGramian matricesgroup framesharmonic frames

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15)

Related Items (10)

The construction of \(G\)-invariant finite tight frames ⋮ Binary Parseval frames from group orbits ⋮ Toward the classification of biangular harmonic frames ⋮ On the construction of highly symmetric tight frames and complex polytopes ⋮ Multiplication-invariant operators and the classification of LCA group frames ⋮ Prime tight frames ⋮ On the number of harmonic frames ⋮ A Characterization of Projective Unitary Equivalence of Finite Frames and Applications ⋮ Unnamed Item ⋮ Tight frames for cyclotomic fields and other rational vector spaces

Cites Work

• Unnamed Item
• The number of harmonic frames of prime order
• On computing all harmonic frames of \(n\) vectors in \(\mathbb {C}^d\)
• Complex equiangular cyclic frames and erasures
• Tight frames generated by finite nonabelian groups
• The symmetry group of a finite frame
• Optimal frames for erasures.
• Tight frames and their symmetries
• Equal-norm tight frames with erasures
• On vanishing sums of roots of unity.
• \(g\)-frames and \(g\)-Riesz bases
• Trigonometric diophantine equations (On vanishing sums of roots of unity)
• Quantized overcomplete expansions in IR/sup N/: analysis, synthesis, and algorithms
• Geometrically uniform frames
• Classification of Finite Group-Frames and Super-Frames
• Automorphisms of Finite Abelian Groups
• On linear relations between roots of unity
• Group Codes for the Gaussian Channel
• THE EULERIAN FUNCTIONS OF A GROUP
• Quantized frame expansions with erasures
• Counting \(p\)-groups and nilpotent groups

This page was built for publication: A classification of the harmonic frames up to unitary equivalence