high & low pass correlated dither noise question I read a pretty cool article the other day: Robert Katz - Dither noise Probability Density Explained.
It says that if you have two dice (A and B) that you can roll both dice and then...

Re-roll die A and sum A and B

Re-roll die B and sum A and B

Re-roll die A and sum A and B

repeat to get a low pass filtered triangular noise distribution.


It says that you can modify it for high pass filtered triangle noise by rolling both dice and then...

Re-roll die A and take A - B

Re-roll die B and take B - A

Re-roll die A and take A - B

repeat to get a high pass filtered triangular noise distribution.


What i'm wondering is, what is the right thing to do if you want to do this with more than 2 dice? (going higher order)
For low pass filtered noise with 3+ more dice (which would be more gaussian distributed than triangle), would you only re-roll one die each time, or would you re-roll all BUT one die each time.
I have the same question about the high pass filtered noise with 3+ more dice, but in that case I think i know what to do about the subtraction order...  I think the right thing to do if you have N dice is to sum them all up, but after each &quot;roll&quot; you flip the sign of every die.
Can anyone illuminate the correct way to do this?
Edit: I'm looking to get high and low pass filtering with more dice, but am fine with the distribution changing from triangle to gaussian or other shapes.
To achieve high-pass shaping , the “DC term” must be 0. Note that in the 2-dice high-pass case, every roll appears twice, once with a positive sign and once with a negative sign, which enforces the DC-free condition.  Any scheme involving more than 2 dice would still need to meet this condition.
The triangular PDF condition is satisfied by the fact that each sum or difference combines 2 rectangular PDF’s. I don’t know how you can get a triangular PDF by combining 3 rectangular PDF’s, regardless of how they are weighted.  

Bob Adams