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Demixing two audio Signals in the time domaine

Started by stef April 13, 2006
Hello experties,
I have the following System in the time domaine that I want to solve with
the unknown x1 and x2:
y1 = h11*x1 + h21*x2   (1)
0 = h12*x1 + h22*x2    (2)
with: h11, h21, h12, h22 are the room impulse responses.
I found the following solution:
x1 = [(h11-h21(h22^-1)h12)^-1]*y1
x2 = -(h22^-1)*h12*x1
I calculated the impulse inverses with the Levinson-Darvin algorithm.
The Problem is:
When i replace the solution in the equations (1) and (2) i found that my
solution verify the following system:
y1 = h11*x1 + h21*x2                (1)
0 = (h22*h22^-1)*h12*x1 + h22*x2    (2')

I will be grateful for each idea that will help me to solve this problem!
Thank you in advance
------
Stef
 
stef wrote:
> Hello experties, > I have the following System in the time domaine that I want to solve with > the unknown x1 and x2: > y1 = h11*x1 + h21*x2 (1) > 0 = h12*x1 + h22*x2 (2) > with: h11, h21, h12, h22 are the room impulse responses. > I found the following solution: > x1 = [(h11-h21(h22^-1)h12)^-1]*y1 > x2 = -(h22^-1)*h12*x1 > I calculated the impulse inverses with the Levinson-Darvin algorithm. > The Problem is: > When i replace the solution in the equations (1) and (2) i found that my > solution verify the following system: > y1 = h11*x1 + h21*x2 (1) > 0 = (h22*h22^-1)*h12*x1 + h22*x2 (2') >
Maybe I'm missing something, but exactly is the problem here? As far as i can see, these two equations are identical to the first two equations. (Assuming all relevant inverses exist.) -- Oli
>stef wrote: >> Hello experties, >> I have the following System in the time domaine that I want to solve
with
>> the unknown x1 and x2: >> y1 = h11*x1 + h21*x2 (1) >> 0 = h12*x1 + h22*x2 (2) >> with: h11, h21, h12, h22 are the room impulse responses. >> I found the following solution: >> x1 = [(h11-h21(h22^-1)h12)^-1]*y1 >> x2 = -(h22^-1)*h12*x1 >> I calculated the impulse inverses with the Levinson-Darvin algorithm. >> The Problem is: >> When i replace the solution in the equations (1) and (2) i found that
my
>> solution verify the following system: >> y1 = h11*x1 + h21*x2 (1) >> 0 = (h22*h22^-1)*h12*x1 + h22*x2 (2') >> > >Maybe I'm missing something, but exactly is the problem here? As far >as i can see, these two equations are identical to the first two >equations. (Assuming all relevant inverses exist.)
They are not exactly the same: (h22*h22^-1) is a shifted dirac impulse :( (* means convolution) Regards -------- Stef
> >-- >Oli > >
stef said the following on 13/04/2006 15:22:
>> stef wrote: >>> Hello experties, >>> I have the following System in the time domaine that I want to solve > with >>> the unknown x1 and x2: >>> y1 = h11*x1 + h21*x2 (1) >>> 0 = h12*x1 + h22*x2 (2) >>> with: h11, h21, h12, h22 are the room impulse responses. >>> I found the following solution: >>> x1 = [(h11-h21(h22^-1)h12)^-1]*y1 >>> x2 = -(h22^-1)*h12*x1 >>> I calculated the impulse inverses with the Levinson-Darvin algorithm. >>> The Problem is: >>> When i replace the solution in the equations (1) and (2) i found that > my >>> solution verify the following system: >>> y1 = h11*x1 + h21*x2 (1) >>> 0 = (h22*h22^-1)*h12*x1 + h22*x2 (2') >>> >> Maybe I'm missing something, but exactly is the problem here? As far >> as i can see, these two equations are identical to the first two >> equations. (Assuming all relevant inverses exist.) > They are not exactly the same: > (h22*h22^-1) is a shifted dirac impulse :( > (* means convolution)
Oh right! I assumed you were treating them as matrices, and so * would be multiplication. h22^-1 is probably not the best notation to use... -- Oli