A new time domain methodology for Computational Aeroacoustics (CAA) is proposed. The time domain wave packet (TDWP) method employs a temporally compact broadband pulse for acoustic sources. As the radiation and transmission of acoustic waves of all frequencies within the numerical resolution are embedded in the propagation of the wave packet, acoustic solution of the full spectrum become available at once. In addition, it becomes possible to separate the acoustic and instability waves in shear flows in the time domain wave packet method due to the compactness of the wave packet. The instability waves can further be suppressed by a source filtering technique, applied after the acoustic wave packet has propagated through the shear layers. Details on the source filtering technique used in the paper are presented. The TDWP method has been validated using a CAA Benchmark problem. The TDWP method is also applied to the NASA/GE Fan Noise Source Diagnostic Test (SDT) exhaust radiation problem.