Hello everyone,
I'm trying to implement an HOA decoder for spherical microphones and I'm
getting some numerical issues :
The principle is the following : I have the temporal signals of all the
capsules of the microphone : it's temporal vector of signals, let's call it
"I" (size n x 1)
I have to multiply this vector by a Matrix "M" (size m x n) to obtain my HOA
components.
So I have to do this operation at each discrete time t :
B = M.I
I've used the solution proposed by Aaron Heller to implement the matrix
multiplication :
// bus with gains
gain(c) = R(c) with {
R((c,cl)) = R(c),R(cl);
R(1) = _;
R(0) = !;
//R(0) = !:0; // if you need to preserve the number of outputs
R(float(0)) = R(0);
R(float(1)) = R(1);
R(c) = *(c);
};
// n = number of inputs
// m = number of output
matrix(n,m) = par(i,n,_) <: par(i,m,gain(a(i)):>_);
a(0) = (0.5, -0.5, 1.1, 1.2,0);
a(1) = (1,2,3,4,-1);
a(2) = (0.5,0.5,0,0.25,1/3);
a(3) = (0,0,0,.1, sqrt(2));
process = matrix(5,4);
It's working but I have got some unexplained numerical problems :
In my matrix "M", the sum of the components of each rows = 0 except the first
row. So if all inputs signals are exactly the same, the outputs will be 0
except the first output.
But, if the signals are not the same, I should have m outputs signals not
null. But I don't when I'm playing my input wav : only the first output is not
null !
So I've tried the following :
I take a constant signal as input signal : the n samples at discrete time t
(extract from my input wav signal)
matrix(n,m)=
(0.143993,0.147716,0.118169,0.141023,0.155442,0.112583,0.166597,0.178432,0.135545,0.186261,0.181142,0.168309,0.137996,0.14302,0.139751,0.157548,0.159706,0.133034,0.168049,0.124931,0.160939,0.161888,0.146289,0.140364,0.188028,0.168121,0.160577,0.152144,0.156805,0.145675,0.196994,0.134682)<:
par(i,m,gain(a(i)):>_);
I measure the output and I've got something everywhere ! But when I play the
wav entirely, no outputs except the first one !
I've implemented this matrix operation in PureData (without the use of Faust)
and it's working when I'm playing the input wav (the M matrix is exactly the
same)
My observations are the following with my Faust code : when the inputs signals
are slightly different, I've got output signal everywhere, but when they are
not exactly identical but close enough, I just have the first output
Here is my Faust code for a M = 3*32 matrix :
import("math.lib");
import("music.lib");
// bus with gains
gain(c) = R(c) with {
R((c,cl)) = R(c),R(cl);
R(1) = _;
R(0) = !;
//R(0) = !:0; // if you need to preserve the number of outputs
R(float(0)) = R(0);
R(float(1)) = R(1);
R(c) = *(c);
};
//vmeter(x) = attach(x, envelop(x) : vbargraph("[unit:dB]", -70,
10));
//envelop = abs : max(db2linear(-70)) : linear2db :
min(10) : max ~
-(80.0/SR);
vmeter(x) = attach(x, envelop(x) : vbargraph("[unit:dB]", -100,
10));
envelop = abs : max(db2linear(-100)) : linear2db : min(10) :
max ~
-(80.0/SR);
// n = number of inputs
// m = number of output
matrix(n,m) = hgroup("Inputs",par(i,n,vgroup("%i",
vmeter)))<:par(i,m,gain(a(i)):>hgroup("Outputs",vgroup("%i",vmeter)));
//matrixtest(n,m) = par(i,n,1) <: par(i,m,gain(a(i)):>_);
//matrixtest2(n,m)=
(0.143993,0.147716,0.118169,0.141023,0.155442,0.112583,0.166597,0.178432,0.135545,0.186261,0.181142,0.168309,0.137996,0.14302,0.139751,0.157548,0.159706,0.133034,0.168049,0.124931,0.160939,0.161888,0.146289,0.140364,0.188028,0.168121,0.160577,0.152144,0.156805,0.145675,0.196994,0.134682)<:
par(i,m,gain(a(i)):>_);
a(0)=(0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125);
a(1)=(0.0505636,0.0460428,0.0505636,0.0460428,0.028456,0.03125,0.0193136,0.03125,0.028456,0.03125,0.0193136,0.03125,0,0,0,0,-0.0505636,-0.0460428,-0.0505636,-0.0460428,-0.028456,-0.03125,-0.0193136,-0.03125,-0.028456,-0.03125,-0.0193136,-0.03125,0,0,0,0);
a(2)=(7.53456*10^-10,0.028456,0,-0.028456,0,0.03125,0.0505636,0.03125,0,-0.03125,-0.0505636,-0.03125,0.0193136,0.0460428,0.0460428,0.0193136,7.53456*10^-10,-0.028456,7.53456*10^-10,0.028456,0,-0.03125,-0.0505636,-0.03125,0,0.03125,0.0505636,0.03125,-0.0193136,-0.0460428,-0.0460428,-0.0193136);
process = matrix(32,25);
//process=matrixtest2(32,25);
Thanks for your help
Pierre Lecomte
PhD student
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