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Inverse matrix

Started by stef March 30, 2006
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
> >