Anechoic sampled instruments and reverberation

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Re: Anechoic sampled instruments and reverberation

Postby dahnielson » Mon Mar 24, 2008 2:46 am

Wow.

I've updated my posts above with additional information and clarification (this is an ongoing research matter -- and I might get things wrong the first time around). But I recommend anyone interested to take a look at the linked Brüel Acoustics, Technical Review 96-02, and the "An acceptable solution" section and onwards in particular.

Sure, it's important to keep in mind that our application is not high precision measuring but fairly low-precision sampling, so there's some leeway as long as we manage to fool our quite gullible auditory system in the end.
Last edited by dahnielson on Mon Mar 24, 2008 3:33 am, edited 1 time in total.
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Re: Anechoic sampled instruments and reverberation

Postby dahnielson » Mon Mar 24, 2008 3:19 am

Just wanted to point out:

Consul wrote:I have an idea for the "Stand of a Thousand Things" to sit in the middle of my room.


No, not in the middle of the room. There's where the big null is. Use the 38% rule.
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Re: Anechoic sampled instruments and reverberation

Postby Consul » Mon Mar 24, 2008 4:00 am

Unfortunately, the middle is the ONLY place anything else in this room can go. The doors to my room are double-wide lightweight fold-outs, so that wall almost doesn't count as a wall. I suppose I could put wheels or slider feet on my Stand of a Thousand Things, so I can move it to better positions for recording, then move it back to the middle.
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Re: Anechoic sampled instruments and reverberation

Postby dahnielson » Mon Mar 24, 2008 12:55 pm

Consul wrote:Unfortunately, the middle is the ONLY place anything else in this room can go. The doors to my room are double-wide lightweight fold-outs, so that wall almost doesn't count as a wall.


Well, if it can't count as a wall (in regards to the room mode and its harmonics) then you're not in the middle of the room (acoustically speaking)! :D

PS. Unrelated: I've added a link to the Beebs Guide to Acoustic Practice (PDF) in the almighty post above.
Last edited by dahnielson on Mon Mar 24, 2008 7:02 pm, edited 1 time in total.
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Re: Anechoic sampled instruments and reverberation

Postby Alex » Mon Mar 24, 2008 1:17 pm

dahnielson wrote:Well, if it can't count as a wall (in regards to the room mode and its harmonics) then your not in the middle of the room (acoustically speaking)! :D



Hehe Anders, now you're being picky. :mrgreen:
Can't fault your logic though!

Alex.
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Re: Anechoic sampled instruments and reverberation

Postby Consul » Mon Mar 24, 2008 1:21 pm

Well, it's a half-wall. Does that mean that it only half-counts towards my room's acoustics? :mrgreen:
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Re: Anechoic sampled instruments and reverberation

Postby Alex » Mon Mar 24, 2008 1:22 pm

Consul wrote:Well, it's a half-wall. Does that mean that it only half-counts towards my room's acoustics? :mrgreen:


Hehe, but is it half left or half right?

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Re: Anechoic sampled instruments and reverberation

Postby dahnielson » Mon Mar 24, 2008 2:09 pm

He he.

What I mean is that if you have two parallel walls with different reflection characteristics in the low end, say one being concrete and the other made out of pink wafers, then the lesser one can be regarded as a false wall and the next wall behind it being used as a reference to figure out where the middle is.

It sounds like your planned setup position is a fairly good one, just remember to try slightly different positions and listen for any abnormal drops or peaks in frequencies. Using your ears instead of fancy theory is usually a winning strategy! :D
Last edited by dahnielson on Mon Mar 24, 2008 7:01 pm, edited 2 times in total.
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Re: Anechoic sampled instruments and reverberation

Postby dahnielson » Mon Mar 24, 2008 2:48 pm

Hemispherical microphone array for capture of sound and radiation pattern

Problem
The main problem is how to capture direct sound in the primary direction of sound radiation regardless its shifting directionality. This can be solved with one of two closely related methods:

  1. Reposition a single microphone depending on tone to be sampled, positioned to capture direct sound in the known primary radiation direction;
  2. Uniformly space microphones around the subject, e.g. at the vertices of a polyhedron, to capture sound that can be used to construct an uniform direct sound recording without previous knowledge about the instruments sound radiation pattern.
The first method only require a regular setup for capturing samples but with knowledge about the type of sound field produced by the instrument to be recorded. The second method require a more extensive amount of gear but with the advantage that any type of sound field can be captured without special knowledge about the instrument. Only the second method will be further discussed.

Objectives
The microphone arrangement will have dual purposes:

  1. To capture the radiated sound to be processed into an approximated point source;
  2. To capture the radiation pattern making reconstruction of it possible.
Requirements
The method require an approximated free-field condition over a reflecting plane to ensure direct sound only capture. A reflecting plane, like concrete, hard wood, parquet or linoleum floor is alright because an orchestra in general lack members with the ability to levitate and move around in the vertical axis. In other words, the distance to the floor is constant and any resulting reflections can be considered part of the approximated point source.

The overall arrangement should not only be limited to capturing of solo instruments, ensembles must work well too, it should just be a matter of scale. The captured ensemble should then be considered as a single instrument on its own.

Microphone Array
A source of inspiration is the theory behind the Ambisonics system and its related recording techniques, arrangement of microphone arrays, encoding and decoding of signals. The microphone array itself produce a first set, the A-format, consisting of the signals from the microphone capsules. These signals are not intended to be used without further processing. The A-format is then transformed into the second set of audio signals, the B-format, consisting of the following four signals:

  • W, a pressure signal (mono) corresponding to the output from an omni-directional microphone;
  • X, the front-to-back directional information, a forward-pointing "figure-of-eight" microphone;
  • Y, the side-to-side directional information, a leftward-pointing "figure-of-eight" microphone;
  • Z, the up-to-down directional information, an upward-pointing "figure-of-eight" microphone.
Encoding and decoding in the Ambisonics system is thus based on spherical harmonics components.

The basic principle of Ambisonics is in our case being inverted: instead of recording at one point, we record the one point. The equivalent of the X, Y and Z signals can be constructed from pairs of facing cardioid microphones while the W signal will be constructed from all microphone signals.

Being able to capture a complete sound field is only useful when the recording space provide a completely approximated free-field condition such as in a full anechoic chamber. Because of the hard reflecting floor, acting as an acoustic mirror, any sound radiated downward will be captured as first-order reflections from above. That is actually how such sound is normally heard! So sound reflected by the floor can in practice be considered being part of the upward sound radiation, the floor will become an integrated part of the sampled instrument.

So what is the least number of microphones needed to capture the radiation pattern and to calculate a pressure signal?

As we only have to cover a hemisphere of sound radiation a set of five microphones pointing 90° to each other will be sufficient, one pair of microphones on the x (front-back) and y (left-right) axis respectively and one mounted directly from above on the positive z (top) axis.

Encoding
Encoding is straight forward with the microphones Cartesian representation. A set of signals containing pressure and directionality information are constructed from the signals captured by the uniformly spaced microphones. Sound pressure W is calculated as the sum of all three signals. The pairs on the x and y axis are summed together to create the X and Y gradient signals respectively, while the single microphone on the z axis signal is kept as Z gradient signal.

W = x1 + (-x2) + y1 + (-y2) + z
X = x1 + x2
Y = y1 + y2
Z = z

Decoding
By combining the WXYZ signals in various proportions it is possible to derive any number of direct sounds, radiating in any direction. In our case create any "virtual microphone" on the surface of the unit hemisphere.

w = sqrt(2)/2
x = cos(A)*cos(E)
y = sin(A)*cos(E)
z = sin(E)

P = W*w + X*x + Y*y + Z*z

P being the output signal, with A and E being angle and elevation, W the pressure signal and X, Y, Z its gradients.

Conclusion
By using a hemispherical microphone array it is possible to encode and decode the radiation pattern of a sampled instrument as well as its sound by the use of spherical harmonics components derived from the theory of Ambisonics. The sampled instrument can then either be treated as an omni-directional point source by ignoring the gradients or having "virtual microphones" placed around it on the surface of the unit hemisphere.
Last edited by dahnielson on Sat Mar 29, 2008 4:39 pm, edited 7 times in total.
Anders Dahnielson

Ardour2, Qtractor, Linuxsampler, M-AUDIO Delta 1010, Axiom 61, Korg D12, AKAI S2000, E-MU Proteus 2k, Roland R-5, Roland HP 1300e, Zoom RFX-1000, 4GB RAM x86_64 Intel Pentium Dual 1.80GHz Gentoo Linux
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Re: Anechoic sampled instruments and reverberation

Postby dahnielson » Sat Mar 29, 2008 1:18 pm

OK, I have edited the post above over the last couple of days along the way with my research and I think I finally nailed it down. It's still unverified and will probably need some practical experimentation. E.g. while the theory of spherical harmonics components and the mathematics behind Ambisonics is solid I'm not sure my inversion and formulae is.

One extension of the method described above, and hinted at in the initial post, is the possibility of only distributing the W signal and create impulse responses (specific to the sampled instrument) to recreate the XYZ signals from the W signal.

The microphone array is one part of my current research related to the issues presented in the initial post. The next step is to figure out how to create an approximated free-field condition over a plane on a limited budget.
Anders Dahnielson

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