Generalised Welch Bound Equality sequences are tight frames
نویسنده
چکیده
This paper shows what are called Welch 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 generalisation 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.
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تاریخ انتشار 2003