  A two-step optimization is proposed to represent an arbitrary quantum state
to a desired accuracy with the least number of gaussians in phase space. The
Husimi distribution of the quantum state provides the information to determine
the modulus of the weight for the gaussians. Then, the phase information
contained in the Wigner distribution is used to obtain the full complex weights
by considering the relative phases for pairs of gaussians, the chords. The
method is exemplified with several excited states n of the harmonic and the
Morse oscillators. A semiclassical interpretation of the number of gaussians
needed as a function of the quantum number n is given. The representation can
also be used to characterize Wigner and Husimi distributions directly which do
not originate in a quantum state.
