Re: Roots() and factorizing large polynomials

[Dupuis]

Borge wrote:
> 
> Hi,
> 
> Im using roots() to factorize a long filter impulse responce
> (polynomial in z). Reassembling the filter from the roots works for
> short impulse responses (see below) but fails for longer ones. Any
> suggestions for better factorization of polynomials?
> 
> The reason I'm doing this is that I want to take a generic FIR filter
> and convert it to a minimum-phase filter. (By finding the roots,
> inverting those with abs()>1, and assembling them to an impulse
> response again.)
> 
> 
Standard roots() algorithm works on a matrix constructed from the polynomial
coefficient. In case some of the roots has a multiplicity greater than one,
the matrix becomes singular. In the case where the distance between two
distinct roots become very small, the matrix becomes quasi-singular, and
roots accuracy is deteriorated.
I use an algorithm written by Prof.  Zhonggang Zeng, where the common
divisor between the polynomial and its first derivative is computed. At this
stage, the number of roots and their multiplicity is computed. Afterwards,
the root finding algorithm is applied on a reduced polynomial containing
only isolated roots with multiplicity one. Accuracy improvement can reach
several orders of magnitude. This material is available at 
http://orion.neiu.edu/~zzeng/multroot.zip
The license is very restrictive :
% This code is freely released for research exchange only. The author 
% is not responsible for any demage caused by using this code.
See if you can cope with it.

Regards

Pascal

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