time – what is the avg DPS of a wave canon and a lock weapon?

I’m trying to show stats of 3 different weapons:

The first weapon is a missile where the damage is instant upon explosion and the DPS is number of missile/s * explosion damage and these two other weapons:

One weapon type is a laser, its damage increases with time from initial DPS at the speed of 0.3 DPS/s up to a max of 8*initial DPS
What’s the average DPS? Or something that’s comparable to a one off DPS weapon like a missile?

The other weapon is like RTYPE wave gun where you keep the button pressed and its damage goes from amp*maxDPS to maxDPS where amp goes from 0.05 to 1 in 1.3 seconds