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Generalized Welch bound equality sequences are tight frames

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1 Author(s)
S. Waldron ; Dept. of Math., Univ. of Auckland, New Zealand

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.

Published in:

IEEE Transactions on Information Theory  (Volume:49 ,  Issue: 9 )