A new multiplex CARS (coherent anti-Stokes Raman scattering) microscopy technique with a single ultrafast laser pulse is demonstrated. All the pump, Stokes, probe pulses are selected inside a single broadband cavity dumping Ti:Sapphire oscillator laser pulse. The measured CARS signal is a coherent sum of the resonant and non-resonant signals, leading to a complicated vibrational line shape due to the spectral interference. The resonant and non-resonant CARS signals, however, have different symmetries in the time domain due to the causality principle of the vibrationally resonant excitation. A new Fourier Transform Spectral interferometry (FTSI) is developed to extract the full complex quantity of the vibrationally resonant signal against the non-resonant one utilizing the different time symmetry. This method can generate Raman-like vibrational spectrum in a single experimental measurement, which can be readily applied to a vibrational hyperspectral imaging. Current sensitivity, available CARS window and application to hyperspectral vibrational microscopy are discussed.