# Demixing two audio Signals in the time domaine

Started by 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!
------
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
```