Beer Budget Beam Steering

Adding FIR filters to have phase control over a wide band of frequencies also means that aplying this to a multiway dipole, we should be able control directivity all the way down to each driver's dipole peak dictated by its baffle width...
Provided of course that each driver has en equivakebt driver iring backwards...
Right?

That is what Patrick is proposing :)
 
I think this technique applies only to lower frequencies, as with rising frequency directivity increases.

No offence meant!

We both agree on that.
And that's why I added that it applies to a source as long as it is considered omnidirectional.
For example, directivity of a 4 inch midrange driver would start manifesting at a much lower frequency than a 3/4 inch tweeter.
Or in other words, the tweeter is omnidirectional at a higher frequency than the midrange driver.
Since another factor that affects directivity is baffle width, the above illustration applies to baffle-less drivers.
 
We both agree on that.
And that's why I added that it applies to a source as long as it is considered omnidirectional.
For example, directivity of a 4 inch midrange driver would start manifesting at a much lower frequency than a 3/4 inch tweeter.
Or in other words, the tweeter is omnidirectional at a higher frequency than the midrange driver.
Since another factor that affects directivity is baffle width, the above illustration applies to baffle-less drivers.

Ok, I see where you're getting at - my english isn't what it used to be :(

The above illustration doesn't, IMHO, apply to baffle-less drivers - it is used regularly in pro audio.
 
Adding FIR filters to have phase control over a wide band of frequencies also means that aplying this to a multiway dipole, we should be able control directivity all the way down to each driver's dipole peak dictated by its baffle width...
Provided of course that each driver has en equivakebt driver iring backwards...
Right?

I'm just doing the math in my head, so I may be wrong here, but I *think* this is how you'd do it with FIR filters:

201505211300419940.jpg

The EAW OTTO is a 32" cube. Measured corner-to-corner, that's a distance of 45.2".

Used without delay, the front and the back driver are going to be in-phase, because the distance is within one-quarter wavelength. (barely.)

h1gPHse.png

But if you delay the front woofer by one quarter wavelength, that's going to give you a cardioid pattern.

6AwusKx.png

WITHOUT FIR filters, that same delay is going to give you a dipole radiation pattern at one octave above the critical frequency. This is because the drivers are separated by one quarter wavelength at the critical frequency AND they're delayed.

To FIX that, we need to HALVE the delay at one octave above the critical frequency.

Here's a comparison of the two options:

WITHOUT FIR Filters:
1) a delay of 3.33 milliseconds, which will line up the wavefronts to create a narrowband cardioid

WITH FIR Filters:
1) a delay of 3.33ms at 75Hz (same as above)
2) a delay of 1.66ms at 150Hz (half as above)
3) I'm not 100% sure what you'd do at 37.5Hz. I have a hunch that the delay would be 6.66ms, but I'm not 100% certain
 
Anyone know if all-pass filters could get the job done?

For instance, if you used an all pass filter that 'peaked' at 37.5Hz, it seems like a plain ol' MiniDSP would do the job here.

I'm not 100% certain if you can combine all-pass filters and conventional low-pass filters in MiniDSP. So if you DID try and do this without using FIR filters, I think you might have to combine a conventional passive low-pass on the woofer, plus a MiniDSP all-pass filter to manipulate the phase response.

allpass_zpssmiavpdi.png



As explained here:

Advanced filters (Allpass/LT etc) with MiniDSP - Car Audio | DiyMobileAudio.com | Car Stereo Forum
 
do you mean you want a 90 degree phase shift from 150Hz down? what do you want to happen above 150Hz? basically the shape of a shelf filter but affecting the phase response instead

No; here's what we want. Assuming a 32" cube, as illustrated in post 28:

WITHOUT FIR Filters:
1) a delay of 3.33 milliseconds, which will line up the wavefronts to create a narrowband cardioid at a critical frequency of 75Hz.
3.33 milliseconds corresponds to the 90 degree phase shift that we require to create a cardioid at a single frequency : 75Hz.

WITH FIR Filters:
1) a delay of 3.33ms at 75Hz (same as above)
3.33 milliseconds corresponds to the 90 degree phase shift that we require to create a cardioid at a single frequency : 75Hz.
2) a delay of 1.66ms at 150Hz (half as above)
1.66 milliseconds corresponds to the 45 degree phase shift that we require to create a cardioid at a single frequency : 150Hz.
3) a delay of 6.66ms at 37.5Hz (twice as above)
This is the one I'm iffy on. To figure this one out, I really need to create a sim.


h1gPHse.png

The easiest way to understand what the goal is, is to understand that we're trying to keep the radiation from the BACK of the loudspeaker in-phase with the FRONT of the speaker. To do this at a single frequency is trivially easy; we just delay the front loudspeaker by a distance equal to the separation between the two drivers.

But doing the same trick at MANY frequencies means that we have to vary the amount of delay of the front speaker.

So we'll have a 'critical' frequency, and the we'll have LESS delay ABOVE that critical frequency, and MORE delay BELOW that critical frequency.

As noted in another post, this is certainly what B&O is doing with the Beolab 90, what Kiii is doing with their flagship, and what Lexicon is doing with Soundsteer.

Lexicon is possibly the most interesting, because it works in the vertical AND the horizontal axis.
Kii is undoubtedly the simplest, as it appears to only function in the bass and midbass.

IMHO, the Kii solution is the best match for DIY, because few of us really care about the variable beamwidth that the Lexicon and B&O solutions can do.
 
Unless I'm missing something, it looks like you can do this with a plain ol' MiniDSP.

Here's how:

G5elyAk.png

As noted in post 31, we need an all-pass filter that creates a rising delay. The exact delays are listed in the last post. (Note that the delay will vary depending on the dimensions of your box. These values are only valid for a 32" cube like the EAW OTTO.)

MiniDSP can do this. The picture above illustrates this. It's fairly simple:
1) put your 'critical frequency' in the cell labeled "Freq"
2) Then vary the Q to get the delay you need. I listed my delay values in post 31. Your delay values will depend on your critical frequency and the dimensions of your box.

vkMTSWa.png

Once you have your values from the spreadsheet, add them to miniDSP as illustrated above. Note that the frequency response does not change; that's the whole point of an all-pass filter.

More instructions here : Advanced filters (Allpass/LT etc) with MiniDSP - Car Audio | DiyMobileAudio.com | Car Stereo Forum

and here :https://www.minidsp.com/forum/softw...ing-an-all-pass-filter-using-advanced-bi-quad


I know this looks daunting, but it literally took ten minutes to get the right values and pop them into my MiniDSP.
 
I enjoy this topic.

With the magic of FIR filters, the only thing that limits beam formation is distance of separation. You can't control frequencies that are significantly larger than your array.

To that point, I don't really buy that the diagonal of the box on the Otto is the relevant distance. Or I suppose more accurately, I think the more complicated model of saying that the box is two perpendicular arrays is no more useful than assuming the front ports and rear ports sum as pairs and you get a directivity bonus for being roughly equivalent to a 32" radiator. That critical 1/4 wave distance is then still limited to 32" from front to back.
 
Last edited:
Sounds like the group delay of a high pass filter may do the job?

I was hoping someone would notice that!

230px-Cardioid_Subwoofer_Array.png


As noted in the previous posts, we need ninety degrees of delay on the front woofer.

But it DOES seem like you achieve this passively, with no DSP whatsoever.

To make this work, you'd need a lowpass filter on the front driver, and a lowpass on the rear driver. But the lowpass on the front woofer would need to be one order HIGHER than the rear.

For instance:
1) 3rd order lowpass on the woofer facing forward
2) 2nd order lowpass on the woofer facing backwards

The additional ninety degrees of phase shift would produce the required delay
 
The FIR filter would only change phase, a lowpass would eat away SPL.
Do we need the same EQ boost on both drivers to make up for that?

One concern that I had with the all-pass filter was that the LOWPASS filter that precedes it would screw up it's phase.

IE, what's the point of using an all-pass filter in MiniDSP if the lowpass filter that precedes it is going to change the phase anyways?

But I realized this isn't an issue as long as the low pass filters used on the front and the rear woofer are symmetrical.

IE, if you use an all-pass on the FRONT woofer, to get cardioid response, and then you precede that filter with a low pass (because this is a subwoofer) then everything is fine as long as you use an identical filter on the rear woofer.



Someone with a better grasp of filters will need to chime in here, but if I'm not mistaken, it doesn't matter if these filters are acoustic or electronic. In other words, you could be creating a low pass using a passive xover, an electronic xover, a DSP xover, or even an acoustic filter like the bandpass box used by EAW, or the rockwool used by Geithain:

ThomasM_Front.jpg


ThomasM_Right.jpg