General questions about PRD skyline diffusors

[azzzy]

I wanna try to make my own diffusors. I spent two weeks reading everything I could find on GS and the rest of the internet. Learned a lot and I think I'm ready. But before I waste a whole bunch of lumber I'd like to confirm a couple of things. Do I understand this correctly:

1. The length of the blocks (well depth) determines the cutoff low frequency (the longer the block the lower the cutoff frequency).
2. The thickness of the block (well width) determines the cutoff high frequency (the thinner the block the higher the cutoff frequency).
3. Does this mean that the longer the blocks and the thinner they are the better the diffusor? (Provided it covers the same area as a diffusor with thicker blocks - as in it uses a higher prime number to cover more area with thinner blocks).

Also is there a specific correlation between the length of the block and the distance from the diffusor to get maximum benefit? I couldn't find anything like that - only that you have to be far enough from the diffusor. How far is enough?

Does the cross section of the block need to be square? Or is rectagular OK too? Is there any benefits to one or the other?

Does the diffusor need to be square? Or can it be rectangular?

Would making the block ends rounded (instead of flat) have any benefit?

I'm planning on trying to build the BBC type diffusor first (doesn't everybody start with that? ). I'm afraid that using regualr 2x2 it won't cover enough area though. If it turns out OK I think I'd make a 17x18 (prime number 307), which with 2x2's should come out about a 28" square.

[Nordenstam]

Originally Posted by azzzy

1. The length of the blocks (well depth) determines the cutoff low frequency (the longer the block the lower the cutoff frequency).
2. The thickness of the block (well width) determines the cutoff high frequency (the thinner the block the higher the cutoff frequency).
3. Does this mean that the longer the blocks and the thinner they are the better the diffusor? (Provided it covers the same area as a diffusor with thicker blocks - as in it uses a higher prime number to cover more area with thinner blocks).

Yes!

Originally Posted by azzzy

Also is there a specific correlation between the length of the block and the distance from the diffusor to get maximum benefit? I couldn't find anything like that - only that you have to be far enough from the diffusor. How far is enough?

Three times the lowest wavelength the diffuser will effect. It can be interpreted in two ways. The most optimistic is to use three times the wavelength of the diffuser depth. The safest is to use three times the wavelength of sound the diffuser wil modify in some way. The diffuser will change the sound in some way even below the design frequency, approximately down to half the design frequency. So, if you want to be absolutely safe, have a distance of six times the design frequency. Or go with the normal three times design frequency.

Originally Posted by azzzy

Does the cross section of the block need to be square? Or is rectagular OK too? Is there any benefits to one or the other?

The square will have the same high frequency cutoff in both direction. The rectangular one will diffuse to a higher frequency in one direction. Both works.

Originally Posted by azzzy

Would making the block ends rounded (instead of flat) have any benefit?

Good question! Don't know. Anyone?

[azzzy]

Thanks for the answers, Lupo.

Originally Posted by Lupo

Three times the lowest wavelength the diffuser will effect. It can be interpreted in two ways. The most optimistic is to use three times the wavelength of the diffuser depth. The safest is to use three times the wavelength of sound the diffuser wil modify in some way. The diffuser will change the sound in some way even below the design frequency, approximately down to half the design frequency. So, if you want to be absolutely safe, have a distance of six times the design frequency. Or go with the normal three times design frequency.

For smaller distances is it better to make a shallower diffusor knowing that it would not do much below a certain frequency or make a deeper one knowing that it would scatter the frequences down to whatever the distance to it allows and the rest will be partially scattered? The reason I'm asking is I have a pretty larger room (24' x 24') but the ceilings are very low - only 7' (and is some places even 6').


I'm thinking of using different prime number for each of my (hopefully) several diffusors. Unfortunately once you get above prime 307 the diffusor will become too heavy to deal with easily. Is it OK to cut the sequence? Essentially if I have a prime number of 599 (23 x 26 matrix) would it be OK to discard 5 rows on the bottom and 8 columns on the right and make it 18 x 18? And perhaps make another diffusor (for the opposite wall maybe) that would use the same matrix but discards 5 rows from the top and 8 columns from the left? Basically the question is: Is there a benefit to making the diffusor with a complete matrix?

[G. E.]

Originally Posted by azzzy

... Is it OK to cut the sequence? Essentially if I have a prime number of 599 (23 x 26 matrix) would it be OK to discard 5 rows on the bottom and 8 columns on the right and make it 18 x 18? And perhaps make another diffusor (for the opposite wall maybe) that would use the same matrix but discards 5 rows from the top and 8 columns from the left? Basically the question is: Is there a benefit to making the diffusor with a complete matrix? ...

Why not make it a perfect 18x17? See complete list of valid pairs of (x, y) for most "quadratic" grids for 2D-PRDs up to 59x60. The main benefit is that you can be sure that it'll work without further investigations.

[azzzy]

Originally Posted by G. E.

Why not make it a perfect 18x17? See complete list of valid pairs of (x, y) for most "quadratic" grids for 2D-PRDs up to 59x60. The main benefit is that you can be sure that it'll work without further investigations.

G.E., thanks for chiming in! I read your entire thread! (spent like half a day reading it). Very helpful thread - I think it should be a sticky. Great job! And those renderings... I don't know how you get them look that great. I learned a lot from reading your thread and wanted to express my appreciation first.

Now onto my topic. Yes, I will certainly make 17 x 18 in its entirety. However I'd like to build several diffusors and I don't want to repeat any pattern twice. Unfortunately as you get higher in the number of blocks/wells the diffusor gets heavier and heavier. I'm also thinking of making the low cutoff freq - 500-600 Hz, which will require longer blocks and make the diffusor even heavier. So to keep the weight manageable I'm thinking of making partial matrixes under 18 blocks per side. Hence my question: is there a benefit to making a complete matrix or it doesn't matter?

[Nordenstam]

Originally Posted by azzzy

For smaller distances is it better to make a shallower diffusor knowing that it would not do much below a certain frequency or make a deeper one knowing that it would scatter the frequences down to whatever the distance to it allows and the rest will be partially scattered? The reason I'm asking is I have a pretty larger room (24' x 24') but the ceilings are very low - only 7' (and is some places even 6').

Don't know if I get the question. You should be fine if you stick to three times the design frequency.

Originally Posted by azzzy

Is there a benefit to making the diffusor with a complete matrix?

Yes! It should be complete to work as intended.

[azzzy]

Originally Posted by Lupo

Don't know if I get the question. You should be fine if you stick to three times the design frequency.

I'll try to rephrase the question (I feel like a lawyer ). If I have a diffusor with 500 Hz cutoff frequency it means I have to be about 7' away from it to get the full benefit. Let's say I'm only 5' away. Does it mean that everything down to 700 Hz still gets diffused properly and then below 700 Hz the diffusion suffers? Or do the frequencies above 700 Hz not get diffused like they would if the diffusor cutoff frequency was 700 Hz?

Originally Posted by Lupo

Yes! It should be complete to work as intended.

Why? I am not questioning you - just want to understand it. The way I see it as long as you keep the sequence and discard only the rows on the edges it should be OK. Isn't the BBC diffusor 12 x 12 when the full matirx is actually 13 x 12?

[Lonely Raven]

azzzy,

Are you downtown Chicago, or are you in the suburbs? Do you have the tools to make all this work?

Just FYI, consider drilling out the wood block to keep the weight down. For example, if you use 1" blocks, get a 1/2" to 3/4" auger type bit and hollow out the block to reduce the weight 25%-50%.

Yes, it doubles the work, but could halve the weight.

[Lonely Raven]

Here is the kind of bit I'm talking about. Electricians and wiring guys use these to put clean holes in framing for running conduit and wiring.



The spiral point will help you hit the exact center of the block without drifting, and you would simply use a piece of tape on the bit to mark the safe depth for a particular size block. For example, take all your 6" blocks, mark a 5" depth on the bit, and go to town. Then take all your 5" blocks, mark 4" depth and go to town. I wouldn't bother for 2" and under though. Not worth the time unless you really need to save weight.

[azzzy]

Originally Posted by Lonely Raven

azzzy,

Are you downtown Chicago, or are you in the suburbs? Do you have the tools to make all this work?

I live in Buffalo Grove right now (never got to changing the location in the profile). I don't own too many tools (come to think of it aside from a hammer and a power dirll - nothing) but a friend let me use his 12" miter saw last night to cut the blocks. Didn't take too long, especially once I clamped 2 2x2's together to cut 2 identical blocks at a time. There are only 4 lengths in the BBC diffusor. If I decide to make another one I will probably clamp 3 2x2's together and get done cutting in under half an hour.

Originally Posted by Lonely Raven

Just FYI, consider drilling out the wood block to keep the weight down. For example, if you use 1" blocks, get a 1/2" to 3/4" auger type bit and hollow out the block to reduce the weight 25%-50%.

Yes, it doubles the work, but could halve the weight.

That's a great idea! Thanks for the tip, Raven. I gotta think about it though. I was gonna put screws through the back at least on some of the blocks (per G.E.'s method). However if the blocks are light enough the screws may not be needed. I made some spare blocks. I will try to hollow out some and see how it works. Thanks.

[Nordenstam]

Originally Posted by azzzy

I'll try to rephrase the question (I feel like a lawyer ). If I have a diffusor with 500 Hz cutoff frequency it means I have to be about 7' away from it to get the full benefit. Let's say I'm only 5' away. Does it mean that everything down to 700 Hz still gets diffused properly and then below 700 Hz the diffusion suffers? Or do the frequencies above 700 Hz not get diffused like they would if the diffusor cutoff frequency was 700 Hz?

The distance is needed for the individual waves from each well to blend into a proper wave front. The diffusion will still work as fine as ever, but you'll be stuck in the near field response of the diffusion - not hearing the proper far field response as it's meant to be.

Here's a simulation of a 1D diffuser:


As can be seen, the area directly in front of the diffuser is a mess. With some distance, the different wave fronts from the various wells converge to a uniform spread of energy. You don't want to be in the messy zone!

Did a very simple and very unscientific test some weeks ago. Let the tap run in the bathroom down the hall, with a trickle of water running into a cup. This made for a nice excitation signal for checking diffuser response! A white noise played through a loudspeaker will possibly do the same. By blocking the ear closest to the sound source, it was easy to hear the reflected energy from the diffuser in the other ear. It's probably a good idea to start off by hearing the reflection from a wall. The comb filtering is obvious! Then try hearing the reflection from a flat panel, hearing how there's a very small zone of tilt where the panel reflects sound directly back at the ear. Then try your new built diffuser. If you're beyond the near field, you'll (hopefully) hear the energy breaking up into zones of high pressure, with smaller pressure in between. It's the "lobing" in diffuser speak. It can be seen in the picture above, where there's sausage like bands of energy with little energy in between. This confirmed for me that the diffuser did work as intended. Also of interest, and on point in this discussion, is that there clearly was a lot of weird things going on in the near field. The slightest movement of the head made the sound change dramatically. Some posters here report good success from using diffusers in the near field. It's probably an individual thing. Though, after doing this test, and listening to music with diffusers close to the sweet spot, I'll keep diffusers at some distance!

Originally Posted by azzzy

Why? I am not questioning you - just want to understand it. The way I see it as long as you keep the sequence and discard only the rows on the edges it should be OK. Isn't the BBC diffusor 12 x 12 when the full matirx is actually 13 x 12?

Also used to believe the BBC diffuser was a dumbed down 13x12 PRD. Turns out it's actually based on several smaller diffusers placed in a pattern that makes for a 12x12 grid. http://downloads.bbc.co.uk/rd/pubs/reports/1990-15.pdf

The goal of diffusion is to scatter sound evenly in all directions. The reason it does this is because the structure is made in the same way as one create white noise. White noise can be checked to be true noise by checking the Fourier response(frequency analysis). If the energy is equal in all frequency bands, it's white noise. Similarly, diffusers can be checked to work as intended by calculating the Fourier response of the array. If a proper sequence is used, the far field response will be flat - like white noise. By omitting one row the result is skewed. It's no longer flat, it'll send more of the sound in some directions than in others.

Lots of technical words there.. Drop a line if you want an explanation without words like Fourier.


Cheers,

Andreas Nordenstam

[G. E.]

Originally Posted by azzzy

... The way I see it as long as you keep the sequence and discard only the rows on the edges it should be OK. Isn't the BBC diffusor 12 x 12 when the full matirx is actually 13 x 12?

I think the well known 12 x 12 BBC diffusor (PRD) design should not be taken for justification of further compromises because its a documented compromise in itself! First: the true grid is 13 x 12, second: the original 12 x 13 = 156 different well lenghts are rounded to just 5 different lengths (0, 1, 2, 3, 4). Whether it's less harming to leave one row out or to intruduce massive lenght rounding, who can tell? For sure there is a difference between a compromised diffusor design and a far less compromised design (12 x 12 BBC vs. 17 x 14 PRD, rounded to 20 different well depths).

EDIT: I remembered incorrectly when I wrote "the true grid is 13 x 12" -- it doesn't hold up to the original BBC-report! -- I hope we can get rid of this misinformation this way.

[azzzy]

Originally Posted by Lupo

The distance is needed for the individual waves from each well to blend into a proper wave front. The diffusion will still work as fine as ever, but you'll be stuck in the near field response of the diffusion - not hearing the proper far field response as it's meant to be.

Originally Posted by Lupo

Some posters here report good success from using diffusers in the near field.

I think what's happening when you're in the near field is you hear the higher frequencies diffused and it sounds different as opposed to a flat wall (or whatever). But does it sound that much different from a diffusor with shallower wells? (as in having a higher cutoff freq)?

Originally Posted by Lupo

Here's a simulation of a 1D diffuser

That's a cool picture. I don't know what it means (for example is this a specific frequency?) but understand it better I'd like to see the same for a flat wall and perhaps for an absorber. Do you have that by any chance?

Originally Posted by Lupo

Also used to believe the BBC diffuser was a dumbed down 13x12 PRD. Turns out it's actually based on several smaller diffusers placed in a pattern that makes for a 12x12 grid. http://downloads.bbc.co.uk/rd/pubs/reports/1990-15.pdf

Which page did you read this on? Because I read the whole thing (I must admit I didn't understand the math. At all. Oh the shame! ) and I didn't see it there. There was a thing about making an array with 1156 wells but they found it too impractical for commercial production. Didn't see anything about the 12 x 12 being a combination of separate matrixes.

Originally Posted by Lupo

The goal of diffusion is to scatter sound evenly in all directions. The reason it does this is because the structure is made in the same way as one create white noise. White noise can be checked to be true noise by checking the Fourier response(frequency analysis). If the energy is equal in all frequency bands, it's white noise. Similarly, diffusers can be checked to work as intended by calculating the Fourier response of the array. If a proper sequence is used, the far field response will be flat - like white noise. By omitting one row the result is skewed. It's no longer flat, it'll send more of the sound in some directions than in others.

OK, I'll be making complete matrixes. I was just given an idea of how to make the bigger diffusors lighter - hollow out the blocks! I'm gonna try it. I just gotta find my vice. Where the hell did I put it?

Originally Posted by Lupo

Lots of technical words there.. Drop a line if you want an explanation without words like Fourier.

Well, I'd love to understand the theory behind it. Why prime numbers, for example? Or what the hell is primitive root? But I'm afraid it's way past my math level. If you manage to lay it out in a way an illiterate immigrant such as myself can understand it I think the community would owe you a debt of gratitude.

[Nordenstam]

Originally Posted by azzzy

I think what's happening when you're in the near field is you hear the higher frequencies diffused and it sounds different as opposed to a flat wall (or whatever). But does it sound that much different from a diffusor with shallower wells? (as in having a higher cutoff freq)?

The distance have nothing to do with frequency, it's about the proper blending of waves. The usual analogy is to multidriver speakers. If you're sitting very close to them, you'll hear one driver more than the other. At some distance the wavefronts from the individual drivers will blend into a single wavefront. That's the minimum distance for that particular speaker. Diffusers are the same, each well acts a sound source and you want to hear the sum of all those sources - not the individual action from each of them.

Originally Posted by azzzy

That's a cool picture. I don't know what it means (for example is this a specific frequency?) but understand it better I'd like to see the same for a flat wall and perhaps for an absorber. Do you have that by any chance?

The size and frequency is unspecified. The frequency was chosen so that it gave the desired effect. We had a great time here in this forum when Terry J came around and started one of the most productive threads ever. It's a hard read since we're all gaining a bit of knowledge here and there, throwing things back and forth across the 9 pages the thread spans. If you start in this post, you'll find exactly what you're asking for! The case for an ideal absorber is very simple - there is no reflection. If you can't be bothered to read far enough to find the videos, here's the direct links: Prime 7 diffuser vs flat wall on Vimeo and 3x prime7 - various frequencies on Vimeo. They'll probably say more than the pics do!

Originally Posted by azzzy

Which page did you read this on? Because I read the whole thing (I must admit I didn't understand the math. At all. Oh the shame! ) and I didn't see it there. There was a thing about making an array with 1156 wells but they found it too impractical for commercial production. Didn't see anything about the 12 x 12 being a combination of separate matrixes.

See the paragraph below figure 4 on page 11. "In a similar way to the more detailed version, this was based on a square array of 12x12 elements, subdivided into smaller sub-sections and quantized into four depths."

If you compare the pattern to a 13x12 PRD, you'll see that it does not corresponds to the pattern minus one coloumn.

The confusing thing is that they also write some lines below: "The absence of the expected null at -(angle of incidence) should be noted. Further study of this theoretical model showed that the principle of assembling smaller Primitive Root Diffusers into a larger module did not work - the result was the same type of behaviour as a Quadratic Residue Diffuser."

I take it that they mean that it did not work in the sense that it did not give suppresion of the specular reflection direction.

Originally Posted by azzzy

Well, I'd love to understand the theory behind it. Why prime numbers, for example? Or what the hell is primitive root? But I'm afraid it's way past my math level. If you manage to lay it out in a way an illiterate immigrant such as myself can understand it I think the community would owe you a debt of gratitude.

It's based on the same formula as used in RSA encryption. The only public key encryption that have not been broken, yet, as far as the general public knows at the moment. Encryption is a game where there's either an unbreakable code or not possible to encode anything that can't be decrypted. At the moment, encryption have the lead. When RSA gets broken we'll have to wait for someone to find another way of doing things before we once again can choose to have privacy. Perhaps it already is broken? We can't know. Those who break the code will keep it secret as long as possible!

The goal is to scramble a given set of numbers (or characters) in a way that can't be deciphered. Prime numbers is an excellent starting point as they can't be divided into anything but themselves and 1. Primitive roots can probably, with some good will, be said to have the same general property. I don't understand it enough to give a simple explanation. Sorry! It doesn't matter much, given that you can use the online calculator here and let the program do the math for you.

Originally Posted by G. E.

I think the well known 12 x 12 BBC diffusor (PRD) design should not be taken for justification of further compromises because its a documented compromise in itself! First: the true grid is 13 x 12, second: the original 12 x 13 = 156 different well lenghts are rounded to just 5 different lengths (0, 1, 2, 3, 4). Whether it's less harming to leave one row out or to intruduce massive lenght rounding, who can tell? For sure there is a difference between a compromised diffusor design and a far less compromised design (12 x 12 BBC vs. 17 x 14 PRD, rounded to 20 different well depths).

I used to think the same way. Have a read at page 11, the upper righthand side, and you'll see the explanation behind the choosen quantization. Makes the unique length for each well approach I did seem like a waste of time..

[G. E.]

Originally Posted by Lupo

... I used to think the same way. Have a read at page 11, the upper righthand side, and you'll see the explanation behind the choosen quantization. Makes the unique length for each well approach I did seem like a waste of time..

You're right, the 12 x 12 BBC diffusor is NOT a shortened 13 x 12 PRD grid -- I'm sorry that I remembered incorrectly. Now I see that indeed there are ways to construct a 12 x 12 grid with smaller PRD grids even without dropping rows (one 12 x 5 grid plus three 4 x 7 grids or plus two 6 x 7 grids). Yet I haven't found a solution with all subgrids being different which would make more sense (now that one makes a nice number theory problem). It's a pity that they don't reveil the actual construction in this paper.

As for the cell depth quantisation: personally I don't get their arguments (the math) apart from the increased manufacturing efforts.