  The intensity of the overlap of a quantum state with all its phase space
translations defines its quantum correlations. In the case of pure states,
these are invariant with respect to Fourier transformation. The overlaps
themselves are here studied in terms of the Wigner function and its Fourier
transform, i.e., the characteristic function or chord function. Unlike the
Wigner function, the chord function need not be real, but eventual symmetry
with respect to reflections about a phase space point may relate these
representations. Semiclassical approximations for the "classical-like" region
of small chords and for large chords are derived. These lead to an
interpretation of the Fourier invariance in terms of conjugate chords. The
interrelation of large and small (sub-Planck) phase space structures previously
noted in the literature are thus reinterpreted.
