  A finite-dimensional Hilbert space is usually described in terms of an
orthonormal basis, but in certain approaches or applications a description in
terms of a finite overcomplete system of vectors, called a finite tight frame,
may offer some advantages. The use of a finite tight frame may lead to a
simpler description of the symmetry transformations, to a simpler and more
symmetric form of invariants or to the possibility to define new mathematical
objects with physical meaning, particularly in regard with the notion of a
quantization of a finite set. We present some results concerning the use of
integer coefficients and frame quantization, several examples and suggest some
possible applications.
