Inverse matrix

Hello, i'm new to this group
I'm trying to demix two audio signal.
My audio signals are y1 and y2 (Y=[y1;y2])
The impulse resonses: H11, H12, H21, H22.
The matrix form of the system is: y=H*x
I'm searching for x: x=(H^-1)*y
The problem is: det(H)=0, also invertible!
i'll be grateful for any idea.

stef said the following on 30/03/2006 13:51:
> Hello, i'm new to this group
> I'm trying to demix two audio signal.
> My audio signals are y1 and y2 (Y=[y1;y2])
> The impulse resonses: H11, H12, H21, H22.
> The matrix form of the system is: y=H*x
> I'm searching for x: x=(H^-1)*y
> The problem is: det(H)=0, also invertible!
> i'll be grateful for any idea.

If det(H) = 0, then H is singular, and so there is no unique solution for x.

In other words, if H is singular, then it implies that y2 can be 
expressed as a function of y1 only, independent of x.

This implies that your system is completely described by:

	y1 = H11.x1 + H12.x2

i.e. one equation in two unknowns, which has an infinite number of 
solutions.


-- 
Oli

stef wrote:
> Hello, i'm new to this group
> I'm trying to demix two audio signal.
> My audio signals are y1 and y2 (Y=[y1;y2])
> The impulse resonses: H11, H12, H21, H22.
> The matrix form of the system is: y=H*x
> I'm searching for x: x=(H^-1)*y
> The problem is: det(H)=0, also invertible!
> i'll be grateful for any idea.

Demixing is usually the task for PCA or better, ICA. Try google search
for independent component analysis.

"stef" <kabbaj@gmx.de> wrote in message 
news:6q-dnSbKc7TRSbbZRVn-qw@giganews.com...
> Hello, i'm new to this group
> I'm trying to demix two audio signal.
> My audio signals are y1 and y2 (Y=[y1;y2])
> The impulse resonses: H11, H12, H21, H22.
> The matrix form of the system is: y=H*x
> I'm searching for x: x=(H^-1)*y
> The problem is: det(H)=0, also invertible!
> i'll be grateful for any idea.

There was some work done along these lines (the objective / not the method) 
using cepstral methods.  The orchestra was removed from a Caruso recording. 
But, that's a lot more sophisticated than the method you are pursuing.

Fred 

>
>"stef" <kabbaj@gmx.de> wrote in message 
>news:6q-dnSbKc7TRSbbZRVn-qw@giganews.com...
>> Hello, i'm new to this group
>> I'm trying to demix two audio signal.
>> My audio signals are y1 and y2 (Y=[y1;y2])
>> The impulse resonses: H11, H12, H21, H22.
>> The matrix form of the system is: y=H*x
>> I'm searching for x: x=(H^-1)*y
>> The problem is: det(H)=0, also invertible!
>> i'll be grateful for any idea.
>
>There was some work done along these lines (the objective / not the
method) 
>using cepstral methods.  The orchestra was removed from a Caruso
recording. 
>But, that's a lot more sophisticated than the method you are pursuing.
>
>Fred 
>
Thanks a lot for your answers,
I've tryed to calculate the inverse impulse responses in the time domain
using Levinson-Durbin Algorithm, and then i transform them to the
frequency domain using fft.
The problem now is that the inverse matrix H^-1 have a complex
parameters.
Any one know what means a complex impulse response matrix?
Thanks.
Stef
>
>