I currently own a two story duplex, which the noise travels between the floors quite clearly. The first noise reduction process would be wall to wall carpet on the upper level with a thick pad (considering if both cost and accessibility are possible). The second and most cost efficient method would be to glue sound board on the existing ceiling on the lower level, then attach resilient channel (or less productive "hat channel")perpendicular to the floor joists. Air pockets between the layers play a critical role as does the proper installation of the resilient channel. After you have that done now you can affix 5/8" drywall to the channel, mud it up and paint! The greatness of this process is you can do one room at a time, when time and money are available, not to mention you don't want to live with your whole house in disarray!