Least Pth Norm Optimal Method

Hello,
I'm interested in papers, articles or books with information on the
application of this method for designing filters. I don't want articles on
using MATLAB. I know how to apply this method using MATLAB. I'm interested
in the underlying theory. Any suggestions? A google search yields only
MATLAB articles.
Thanks

On Jul 1, 2:40 pm, "Kral" <jd_l...@yahoo.com> wrote:
> Hello,
> I'm interested in papers, articles or books with information on the
> application of this method for designing filters. I don't want articles on
> using MATLAB. I know how to apply this method using MATLAB. I'm interested
> in the underlying theory. Any suggestions? A google search yields only
> MATLAB articles.
> Thanks

There are some paper on adaptive filters (LMS) extending ordinary
least-mean squares.
Widrow looked at this a long time back.

K.

Kral wrote:
> Hello,
> I'm interested in papers, articles or books with information on the
> application of this method for designing filters. I don't want articles on
> using MATLAB. I know how to apply this method using MATLAB. I'm interested
> in the underlying theory. Any suggestions? A google search yields only
> MATLAB articles.

Indeed, an interesting question: why would one chose one "p" over
another? Consider the example of "fitting" FIR filters to a target
frequency response. For p=2, one can apply a rectangular window to the
impulse response. However, the resulting ringing (see the resecnt
thread about Gibbs) is usually not acceptable, meaning that p=2 is not
an optimal choice. For matching non-noisy target frequency responses,
I would use a larger p's, for example p=infinty (minimax filters).

However, for fitting noisy frequency responses (for example in non-
parametric frequency domain system identification), p=2 combined with
a weighting scheme that takes care of the uneven "information
distribution" for excitation signals with non-flat frequency response
might be a good choice (in fact, it might be the best choice from a
statistical point of view). If more is known about the distribution of
the frequency domain noise, it might even be sensible to not minimize
a p-norm, but some other error functional. A well-known error
functional that is not a p-norm is based on minimizing p=2 for small
residues and p=1 for large residues.

Some of the noise aspects are discussend in Ljung's already classic
book [1]. There is a lot of literature on desigining minmax filters
(IIR and FIR). If you are interested in the statistical properties of
different p's (and other error functionals), look for M-estimators.

Regards,
Andor

[1] Lennart Ljung, System identification: theory for the user (second
edition); Prentice-Hall, Englewood Cliffs, NJ, 1999, ISBN
0-13-656695-2.