  Finite frame theory has become a powerful tool for many applications of
mathematics. In this paper we introduce a new area of research in frame theory:
Integer frames. These are frames having all integer coordinates with respect to
a fixed orthonormal basis for a Hilbert space. Integer frames have potential to
mitigate quantization errors and transmission losses as well as speeding up
computation times. This paper gives the first systematic study of this
important class of finite Hilbert space frames.
