  Harmonic inversion has already been proven to be a powerful tool for the
analysis of quantum spectra and the periodic orbit orbit quantization of
chaotic systems. The harmonic inversion technique circumvents the convergence
problems of the periodic orbit sum and the uncertainty principle of the usual
Fourier analysis, thus yielding results of high resolution and high precision.
Based on the close analogy between periodic orbit trace formulae for regular
and chaotic systems the technique is generalized in this paper for the
semiclassical quantization of integrable systems. Thus, harmonic inversion is
shown to be a universal tool which can be applied to a wide range of physical
systems. The method is further generalized in two directions: Firstly, the
periodic orbit quantization will be extended to include higher order hbar
corrections to the periodic orbit sum. Secondly, the use of cross-correlated
periodic orbit sums allows us to significantly reduce the required number of
orbits for semiclassical quantization, i.e., to improve the efficiency of the
semiclassical method. As a representative of regular systems, we choose the
circle billiard, whose periodic orbits and quantum eigenvalues can easily be
obtained.
