How to change the damage per second formula?

Question

Mathematics

There is a fighter who has a regular punch.
Hit stats : Base Damage Damage , Crit Chance CritChance , CritMultiplier and AttackSpeed ​​.
Damage per second formula:

CritDamage = Damage * CritChance * CritMultiplier
NormalDamage = Damage * (1 - CritChance )
DPS = (NormalDamage + CritDamage) * AttackSpeed

​​Now every N seconds, instead of a normal hit, a new super hit occurs, which increases damage by SuperDamageMultiplier. A super hit can be a critical hit like a normal hit.

How to add a super hit to the DPS formula?

Update
With these data:
Damage = 100
CritChance = 0.3
CritMultiplier = 2
AttackSpeed ​​= 5

SuperDamageMultiplier = 10
N = 3

Average DPS in experiments 1000

Answer 1

One hit in N seconds is replaced from normal to super. We get:

DPS * N = (NormalDamage + CritDamage) * AttackSpeed * N
        - (NormalDamage + CritDamage)
        + (NormalDamage + CritDamage) * SuperDamageMultiplier
= (NormalDamage + CritDamage) * (AttackSpeed * N - 1 + SuperDamageMultiplier)

DPS = (NormalDamage + CritDamage) * (AttackSpeed + (SuperDamageMultiplier - 1) / N)

Answer 2

+Normal Damage*SuperDamageMultiplier/N
if super damage can be for crit, add it separately

Answer 3

DPS2 = ((NormalDamage + CritDamage) * AttackSpeed) * SuperDamageMultiplier / N