  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 with members
ordered according to energy concentration after half sample shifts; the primary
(first) member being the global optimum.
