Generalized Welch bound equality sequences are tight frames

Authors:
S. Waldron
Affiliations:
Dept. of Math., Univ. of Auckland, New Zealand
Venue:
IEEE Transactions on Information Theory
Year:
2006

Citing 0
Cited 3

An Introduction to Frames

Foundations and Trends in Signal Processing
A Criterion for Attaining the Welch Bounds with Applications for Mutually Unbiased Bases

Mathematical Methods in Computer Science
Constructing and decoding GWBE codes using Kronecker products

IEEE Communications Letters

Quantified Score

Hi-index	754.84

Visualization

Abstract

This article shows what are called the Welch (1974) bound equality (WBE) sequences by the signal processing community are precisely the isometric/equal norm-normalized/uniform tight frames which are currently being investigated for a number of applications, and in the real case are the spherical 2-designs of combinatorics. Recent applications include wavelet expansions, Grassmannian frames, frames robust to erasures, and quantum measurements. This is done by giving an elementary proof of a generalization of Welch's inequality to vectors which need not have equal energy, and then showing that equality occurs in this exactly when the vectors form a tight frame.