Maximally Concentrated Sequences After Half-Sample Shifts
Karim Said, A.A. Beex, Lingjia Liu · IEEE Signal Processing Letters · 2024
It is well known that index (discrete-time)-limited sampled sequences leak outside the support set when a band-limiting operation is applied. Similarly, a fractional shift causes an index-limited sequence to be infinite in extent due to the inherent band-limiting. Index-limited versions of discrete prolate spheroidal sequences (DPSS) are known to experience minimum leakage after band-limiting. In this work, we consider the effect of a half-sample shift and provide upper bounds on the resulting leakage energy for arbitrary sequences. Furthermore, we find an orthonormal basis, derived from DPSS, whose members are ordered according to energy concentrationafter half sample shifts; the primary (first) member being the global optimum.