Tom
11-06-2003, 04:42 AM
Suppose we have two signals - a Primary and Reference as in classical
noise cancelling except that the mics are about one foot apart (for an
acoustic problem). Let us suppose that the top path (for simplicity) has
a transfer function (1-0.5z^-1) and the bottom path has a TF of unity.
This of course is not realistic but I want to keep the sums easy. Now if
we use LMS the LMS algorithm will converge nicely to (1-0.5z^-1) -
assuming there is no additive noise.
Now consider the same problem but with a TF in the top path of (Primary)
of (1-2z^-1). Again the LMS algorithm has no trouble identifying this.
The problems occur when the TF is in the bottom path. In the Min Phase
case the LMS algorithm will converge to the inverse of (1-0.5z^-1) =
1-0.5z^+0.25z^-2-... ie the inverse.
For the Non Min Phase case the inverse gives us a non-convergent series
and the LMS algorithm runs into trouble.
Is there an answer to this other than reversing the mics?
Thanks
Tom
noise cancelling except that the mics are about one foot apart (for an
acoustic problem). Let us suppose that the top path (for simplicity) has
a transfer function (1-0.5z^-1) and the bottom path has a TF of unity.
This of course is not realistic but I want to keep the sums easy. Now if
we use LMS the LMS algorithm will converge nicely to (1-0.5z^-1) -
assuming there is no additive noise.
Now consider the same problem but with a TF in the top path of (Primary)
of (1-2z^-1). Again the LMS algorithm has no trouble identifying this.
The problems occur when the TF is in the bottom path. In the Min Phase
case the LMS algorithm will converge to the inverse of (1-0.5z^-1) =
1-0.5z^+0.25z^-2-... ie the inverse.
For the Non Min Phase case the inverse gives us a non-convergent series
and the LMS algorithm runs into trouble.
Is there an answer to this other than reversing the mics?
Thanks
Tom