  In this paper, we investigate the influence of the symmetry of the biphoton
wavefunction on the coincidence measurement of the generalized Mach-Zehnder
(MZ) interferometer, where there are a temporal and frequency shift operations
between the two beam-splitters. We show that the generalized MZ interferometer
is the measurement of the short-time Fourier transform of the function modeling
the energy conservation of a spontaneous parametric down-conversion process if
the full biphoton state is symmetric, and of the symmetric characteristic
distribution of the phase-matching function if the state is antisymmetric.
Thus, this technique is phase-sensitive to the spectral distribution of the
photon pairs. Finally, we investigate in detail the signature of a pair of
anyons whose peculiar statistics can be simulated by engineering the spectrum
of photon pairs.
