HOA Tutorial Exercise 02

Extension

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In order to correctly reconstruct a sound field from the channels of the B-format, it is important to know about standard normalisation methods for the spherical harmonic components, as well as channel ordering conventions. Two main channel ordering conventions exist:

FuMa

The original Furse-Malham higher-order format, an extension of traditional second order B-format up to third order (16 channels). See: https://en.wikipedia.org/wiki/Ambisonic_data_exchange_formats#Furse-Malham. FuMa channel ordering comes with maxN normalization. See: https://en.wikipedia.org/wiki/Ambisonic_data_exchange_formats#maxN. The FuMa format has been widely used and is still in use but is increasingly replaced by:

ACN

The Ambisonic Channel Number (ACN) ordering has reached wide consensus for future higher-order systems. See: https://en.wikipedia.org/wiki/Ambisonic_data_exchange_formats#ACN, and compare with the image from Exercise_01_HOA_b_format.

Channel numbers and names up to order 3:

B-formats above order 3 typically follow the ACN convention.

The normalization options for ACN are:

N3D

In the full three-D normalisation, all signals are orthonormal. This has advantages for transformations of the B-format, which rely on its orthonormality (XYZ rotations, beamforming, etc. ). See: https://en.wikipedia.org/wiki/Ambisonic_data_exchange_formats#N3D.

SN3D

The Schmidt semi-normalisation has the advantage that none of the higher order signals exceeds the level of the W channel (ACN 0), which is useful when monitoring levels in recording situations. See: https://en.wikipedia.org/wiki/Ambisonic_data_exchange_formats#SN3D.

The examples below show the difference of the three b-format conventions with respect to channel ordering and normalization the supported combinations are:

• ACN N3D
• ACN SN3D
• FuMa MaxN

In case you have not done so yet: let's start the sound server, which we configure first to get more audio buses and 36 output channels.s.quit; // quit the server first if it is still running ( ServerOptions.devices; s = Server.local; Server.local = Server.default; o = Server.local.options; // Get the local server's options o.numInputBusChannels = 2; // Set Input to number of Inputs o.numOutputBusChannels = 36; // lets start after chan 36 so as not to see the mic input o.numAudioBusChannels = 1024 * 2; // default is 1024 o.blockSize = 512; o.numWireBufs = 64 * 16; // for more complex SynthDefs o.memSize = 2.pow(16); // default 2.pow(13) o.sampleRate = 48000; s.makeWindow; s.boot; )

Start the oscilloscope showing all the channels for the selected order of the b-format.( // try different orders up to 5 ~order = 4; ~hoaNumChannels = (~order+1).pow(2); s.scope(~hoaNumChannels); )

Let's use a proxy for the creation of a B-format signal:( ~hoaSignal = NodeProxy.new(s, \audio, ~hoaNumChannels); ~hoaSignal.source = {HOAEncoder.ar(~order, WhiteNoise.ar(1), pi* 0.25, pi* 0.25 )}; ~hoaSignal.fadeTime = 1; ~hoaSignal.play(0, ~hoaNumChannels); )

Change between normalization within ACN and compare the amplitudes of the channels in the oscilloscope.~inFormat = \ACN_N3D; // try all three different out formats ~outFormat = \ACN_SN3D; ~outFormat = \ACN_N3D; ~outFormat = \FuMa; ~hoaSignal.source = {HOAConvert.ar(~order, HOAEncoder.ar(~order, WhiteNoise.ar(1), pi* 0.25, pi* 0.25 ), ~inFormat, ~outFormat)};

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Next: Exercise_03_HOA_decoding_for_monitoring