DPS was calculated as [Damage Rating] * [Rate of Fire].
For example, the Unpacked QoT at level 20 has 306 Damage Rating and ~0.92 Rate of Fire. Her DPS is 306 * 0.92 = 280 DPS.
If you have attack speed DPS is calculated as [Damage Rating] / [Attack Speed].
For example, the Unpacked QoT at level 20 has 306 Damage Rating and 1.09 Attack Speed. Her DPS is 306 / 1.09 = 280 DPS.
Another tidbit of interest is that items that increase attack speed are percent based. This means that the higher your base RateofFire (or the lower your attack speed), the greater the gain from +attack speed buffs. Rate of Fire is capped at 2 (1 attack every 0.5 seconds). So the Unclean Beast gains around ~15% more DPS from attack speed buffs than the Rook does (until the cap of is reached). Likewise demigods with high Rates of Fire gain more DPS from +damage items (they hit more often and gain the same benefit per hit).