Question about Diffusor plan equations

[Skrasms]

I understand how to use quadratic residue and such to make a diffusor based on the BBC articles, but there's one thing I can't help but wonder: what makes a quadratic residue sequence better than just using a sequence of completely random numbers between two boundaries? Shouldn't the scattering of a diffusor be as random as possible? Or does it turn out that using quadratic residue creates some type of symmetry to make the diffusion spread out more evenly, and that is more important? I hope my question makes sense.

[barefoot]

Hi Skrasms and welcome!

This is a really good question. I only wish I had a good answer!

My background is in experimental physics, not mathematical physics, but let me take a qualitative crack at it. I'm pretty sure that, in theory, you are right. A random surface will produce diffuse reflections. The issue, however, comes down to practicality.

All random sequences have some level of short scale periodicity. In other words, for a small number of rolls of the dice, there is some low order linear function that will fit the data. The elements in the sequence appear not to be random, only because there are so few of them. A surface having this sort of short scale linearity will not produce diffuse reflections. But we need to physically build this diffuser. We don't want it to be too complex. And it turns out that a dozen or so random surface elements just aren't random enough. We would need a lot more per unit length to get the results we want. So the real beauty of the Schroeder residue approach is that it allows us to use a relatively small number of surface elements to achieve a high level of diffusivity.

I haven't investigated diffusors in theoretical detail, so I might be wrong. But, I'm pretty sure this is the gist of it.

Thomas

[VSpaceBoy]

So if I understand.. The use of the formula creates a more random than random surface? <so to speak>

[barefoot]

No, not really. Think of it as a periodic surface with the special properties of giving diffuse reflections over a limited frequency range.

[Jim B]

... Shouldn't the scattering of a diffusor be as random as possible? Or does it turn out that using quadratic residue creates some type of symmetry to make the diffusion spread out more evenly, and that is more important? I hope my question makes sense.

I haven't mastered the QRD concept....but, good diffusion needs to have certain qualities that make it a good diffusor design.

1) It needs to reflect the scattered sound in all directions (3 dimensional). I can kind of understand why a repeated pattern would be advantageous to retain the stereo imaging.

2) It should not be absorptive. Some QRD diffusors will actually reasonate and absorb lower frequencies. Diffusors should diffuse.

3) Good diffusion works. Acoustically, it has the perceived effect of moving the wall surface farther away from the listening position...and knocks out slap back and flutter echos.