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From: cfy30 on 11 Jul 2010 23:37
Hi all,

w(n+1) = w(n) + mu*e(n)*x(n)

Can anyone tell me how to determine the maximum mu? I read some materials
that mu should be less than 2/lambda_max, where lambda_max is the maximum
eigen value of the autocorrelation matrix of the input.

Take the 50Hz noise cancellation filter in Widrow's paper as an example,
"Adaptive Noise Cancelling : Principles and Applications". How to determine
the maximum mu?


Thanks,
cfy30

From: HardySpicer on 13 Jul 2010 23:10
On Jul 12, 3:37 pm, "cfy30" <cfy30(a)n_o_s_p_a_m.yahoo.com> wrote:
> Hi all,
>
> w(n+1) = w(n) + mu*e(n)*x(n)
>
> Can anyone tell me how to determine the maximum mu? I read some materials
> that mu should be less than 2/lambda_max, where lambda_max is the maximum
> eigen value of the autocorrelation matrix of the input.
>
> Take the 50Hz noise cancellation filter in Widrow's paper as an example,
> "Adaptive Noise Cancelling : Principles and Applications". How to determine
> the maximum mu?
>
> Thanks,
> cfy30

I could tell you but then I would have to shoot you.
Best to use NLMS.


Hardy
From: robert bristow-johnson on 14 Jul 2010 00:53
On Jul 13, 11:10 pm, HardySpicer <gyansor...(a)gmail.com> wrote:
>
> I could tell you but then I would have to shoot you.

....

> Best to use NLMS.

so now are you gonna shoot him?

r b-j

From: maury on 14 Jul 2010 09:28
On Jul 11, 10:37 pm, "cfy30" <cfy30(a)n_o_s_p_a_m.yahoo.com> wrote:
> Hi all,
>
> w(n+1) = w(n) + mu*e(n)*x(n)
>
> Can anyone tell me how to determine the maximum mu? I read some materials
> that mu should be less than 2/lambda_max, where lambda_max is the maximum
> eigen value of the autocorrelation matrix of the input.
>
> Take the 50Hz noise cancellation filter in Widrow's paper as an example,
> "Adaptive Noise Cancelling : Principles and Applications". How to determine
> the maximum mu?
>
> Thanks,
> cfy30

For the LMS algorithm:

1. Define a weight-error vector
2. Write the weight-error vector as a recursive algorithm in terms of
the auto-correlation matrix of the input
3. Perform a unitary-similarity transformation on the auto-correlation
matrix
4. Rotate the weight-error coordinate system using the eigenvector
matrix of the unitarity-similarity transformation
5. Observe what must occur for convergence
6. QED

Or, you could spend some time and look it up in one of several books:

[1] Clarkson, Peter M. "Optimal and Adaptive Signal Processing"
[2] Widrow, Bernard, and Stearns, Samuel, "Adaptive Signal Processing"
[3] Hatken, Simon, "Adaptive Filter Theory"
[4] Graupe, daniel, "Time Series Analysis"

If you look at the normalized LMS (NLMS), then the maximum mu is
limited to the sum of the number of filter coefficients. That proof I
will leave to you.

Maurice Givens
From: Vladimir Vassilevsky on 14 Jul 2010 10:35


maury wrote:


> If you look at the normalized LMS (NLMS), then the maximum mu is
> limited to the sum of the number of filter coefficients.

IMO what does matter is optimim rather then maximum. You need to
minimize the total error of the process. This error is because of
imperfect adaptation, noisy gradients, nonlinearity, ambient noise and
numeric artifacts. It also depends on the statistics and power of the
reference signal. So the algorithm must adapt Mu in pseudo Kalman way.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com
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