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.

# Inverse matrix

Started by ●March 30, 2006

Reply by ●March 30, 20062006-03-30

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

Reply by ●March 30, 20062006-03-30

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.

Reply by ●March 30, 20062006-03-30

"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

Reply by ●March 30, 20062006-03-30

> >"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 themethod)>using cepstral methods. The orchestra was removed from a Carusorecording.>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> >