  A geometric perspective involving Grammian and frame operators is used to
derive the entire family of Welch bounds. This perspective unifies a number of
observations that have been made regarding tightness of the bounds and their
connections to symmetric k-tensors, tight frames, homogeneous polynomials, and
t-designs. In particular. a connection has been drawn between sampling of
homogeneous polynomials and frames of symmetric k-tensors. It is also shown
that tightness of the bounds requires tight frames. The lack of tight frames in
symmetric k-tensors in many cases, however, leads to consideration of sets that
come as close as possible to attaining the bounds. The geometric derivation is
then extended in the setting of generalized or continuous frames. The Welch
bounds for finite sets and countably infinite sets become special cases of this
general setting.
